@@TommyBo42 Not "but it approaches infinity". Instead, "something" approaches infinity. That something is actually "something else" ppl dont understand unless they have knowledge of math analysis.
@@TommyBo42 no if f(x)=1/x .. as x increases or approaches infinity f(x) gets smaller ..if x goes towads zero f(x) increases .. but f(x)is Undefined for x=0 ..it makes as much sense as take the Inverse sine of 2 wich is undefined
I thought about it like this. At the beginning there is one right-handed person in the room. How many left-handed people do I need for there to be 2% right-handed people in the room? Clearly I need 49. Therefore I have to remove 50 left-handed people. I did all this in about 5 seconds.
yeah, it's easiest and fastest to turn the percentage of right-handed people into a ratio to all people in the room. I thought about it about the same: 1% is 1:100, and then 2% is 2:100, or 1:50. to get from 1:100 to 1:50, you take away 50 left-handed people.
I realized immediately that just removing a person would result in a non-integer percentage, but it took me a while to realize what else to do. But I'm proud to say I got the answer before he said it!!!
ya, took a min realise what was asked... but its easier calculate on those right handed u want right handed to be 2% ot the total left in the room -> 1/.02=50 ppl must be left in the room ..would had been fun if thay asked how many have to leave to bring it down to 97%
I'm glad to see that a lot of people didn't go through the entire process, and rather know or have come to the conclusion that in order to double the percentage of right-handed people, you need to halve the total number.
Hello. I've only began to pursue math recently after a long break since the end of school. This problem did not come intuitively at all for me, do you have anything you would recommend beside doing more of these, or is it just a natural talent I don't have?
@@TroySturges-g6u make excel spreadsheets about video games with respect to crit chance, crit damage, attack speed, damage mitigation, effective total health etc. You'll get intuitive about percentages real quick
That is going through the entire process, only very quickly. When you solve in your head, you go through all the steps, just without spending so much time writing.
That is a superb analysis from you there. The quiz show that this question is from i was watching when aired, i was furious that i got it wrong, but your lesson there im gunna remember for future maths questions.
I thought about it like this: When you want 100 people with 98% left handed, you need 98 left handed and 2 right handed people. Then I divided both by two so there’s only one right handed person. That left me with 49 left handed people. And 99-49=50, so 50 left handed people have to leave.
@@TrentRProductions Lol, I was reading the comments while assuming the video gave the quick solution. But now I took a look at the video and it is truly horrible, lol.
I calculated it using some algebra. The original percentage of 99% is 99 left-handed people out of 100 people in total. If we represent the number of left-handed people that will leave the room with “x”, then we have (99 - x)/(100 - x) = 98% (the new percentage we are looking for) = 0.98. Once you work it out, you get x = 50.
@@ronald3836now tell me how many people need to leave for the percentage to be below 93.5%. You can’t do that just by looking at it but the formula still holds up. Maybe think for a second why what he is doing might be important
The Percentile quantities were Supposed to Confuse the Reader, as some commenters STATED, it's Best to make a Formal Computation rather than Follow a Seemingly Logical answer...😊😎👍
Go in the opposite direction: start with 1 right-handed person. How many lefties do you need to bring in to the room to get to a ratio of 100:2 (given that the max number of righties is 1)?
This is the first one on your videos that I figured out immediately. My brain went to one person is 1% in the initial scenario, so for someone to be 2% of the group there would need to be half the total people.
@@JuergenW. the concept of the original show is the questions get harder based on how many people are able to answer them, and the final question is supposed to be answerable only by 1% of people. They have a panel of 100 people answering the questions along with the contestant and you see how many of them go out on each question. Of course, it doesn't mean the same 1% will be able to answer all of the 1% questions on the show. Some, like this one, I find quite easy. Others are more complicated.
04:47 It would be easier to calculate this, if we would firstly multiply both sides by 100 (to get 100=2*x), and secondly divide both sides by 2 (to get 100/2 = x and x=50).
I used a slightly different method. 99 are left handed so that means 1 is right handed. 1 out of 100 equals 1% 1 out of 50 total equals 2%. That means 50 less Total people.
Very nice demonstration. I went the other way. The number of rightanded is constant, always 1. If 98% are lefthanded then 2% are right handed. The total number of people to have 1 person be 2% is 2/100=1/x -> 2=100/x -> 2x=100 -> x=50. W started with 100 people, so (100-50) = 50 has to leave.
1 in a 100 (1+ 99 (%)) must go to 2 in a 100 (2 + 98(%)). But we had only 1 righthanded, so 2 and 98 divided by two (in order to get 1 righthander), leaves 49 lefthanders. We had 99 lefthanders, so 50 have to go...😊
As others have pointed out, I solved it by thinking how many people in total they had to be for one person to equal 2%, which is one out of fifty (so 49 others). Thus simply 99-50 = 49. But I appreciate the more algebraic solution to the general problem, where the numbers might be harder to think about in your head.
The solution in the video seems sooo complicated almost as if you were searching for the most complex way possible The most straightforward and obvious solution for me is to realize this: We have one person which makes 1% of the total amount of group. 1/0,01 = 100 Now, that same one person should make 2% which means: 1/0,02 = 50 That's it. No more complications with equations or anything
Quick intuitive approach - equation balancing, you want to double the number of right handed people, inversely, you need to half the number of left handed.
You need to halve the total number of people in the room! Your stated approach 99/2=49.5 is a bit brutal and doesn't solve the problem! ( Not questioning your reasoning, you didn't word it right! )
@alexandergutfeldt1144 correct, I didn't want to write an essay. I left out the parts of keeping the total number of people at 100 by converting the lefts to rights, reducing by the desired ratio (accidental time stamp), then converting back with the new group. Thanks for keeping me honest, I lazy math often.
@@alexandergutfeldt1144 are you stoo-pid ?? He clearly wrote "quick INTUITIVE approach" He didn't write "correct calculation" Do you ever get invited to social events?
Another problem is asking how to bring the percentage down to 96%. The answer is 75 left-handed people must leave the room leaving 1 right-handed person and 24 left-handed people. 24 out of 25 is 96%. The easier way to calculate this is to concentrate on the number of right-handed persons which is always one. 1=4x/100 which equals 25 so there are 24 left-handed and 1 right-handed so 75 of 99 left-handed must leave the room. In the problem given the equation would be 1=2x/100 which equals 50 so there is 1 right-handed and 49 left-handed (49 out of 50 is 98%) so 50 left-handed must leave the room. This math is easier than what is shown.
Took me ages to realize if people leave there would no longer be 100 people... Once this was clear, answer became obvious. In a TV show I would have panicked.
Answer should. Be 50 .. Initially we have 99 left handed person and 01 right handed person .. in the scenario we did not change no. Of right handed person that is 01 according to required condition 01 should be 2% of total persons in the room so 49 person will be 98% sir that 50 person have to left eoom
I read the thumbnail and immediately started guessing n/(n+1) values until I found the answer, then I started the video. The algebraic method and logic makes a lot of sense!
I solved it mentally with algebra. The hardest part was remembering the numbers, keeping them in mind. Here ‘s the equation: 99-x/ 100-x = 98/100. It took me more than 30 seconds to do it, though. Still, not bad for an octogenarian!
If 98% are left-handed, then 2% must be right-handed. 2. In the room, there’s only 1 right-handed person, and that 1 person represents 2% of the total number of people after some have left. 3. To figure out the total number of people, you ask: • “What total number of people makes 1 equal 2%?” • The answer is: 100% ÷ 2% = 100 ÷ 2 = 50.
50 people, 99/100 is 99% 49/50 is 98% Kevin of Vsauce2 covered this exact thing albeit with a different premise (something to do with potatoes iirc). You can also look at it the other way round, there is 1 right handed person 1 out of 100 is 1% you need it to be 2% so 1/0.02 (or 100/2) which is 1 out of 50
I see this proportion on a screen is the proper way, but I solved it like that: Basically: 100 = 100*0.98 + r (r - the number of right-handed people, we know it's 1 very easily, but for the sake of demonstration) And in the new case: N = N*0.98 + R (N - the new total number of people, new R just for the demo) At the same time: N = 100 - Ld + R (Ld - the lefties number difference from the original 100) So we substitute: 100 - Ld + R = (100 - Ld + R)*0.98 + R 100 - Ld = 98 - 0.98Ld + 0.98R 2 - 0.98R = 0.02Ld (we know R = 1 though, otherwise no go) 1.02 = 0.02Ld Ld = 51 - number of lefties should leave, so overall it will be 50 people
Easier mathematical manipulation if you recast as right-handed percentage. 1 right-handed person in the room with 99 left-handed is 99% left handed or 1% right handed. So to go down to 98%-left is to go up to 2%-right. Equation is almost the same but much quicker to solve since there is always 1 right handed peron and "x" left-handed people need to leave ther room 1/(100-x) = 0.02 Note it is easier if you recall that 0.02 = 2/100 = 1/50 1/(100-x) = 1/50 So 100-x = 50. x=50
to try to solve it within 30 seconds a viable option is 98% = 98/100 reduce this fraction 49/50 luckily the original condition was 99/100 = 99% so removing 50 from numerator and denominator (removing 50 left handed people removes 50 from total) leads to 98% looking at the comments, the 1% to 2% trick is even better (thinking of the complement, amount of right handed people) 1/100 2/100 = 1/50 (so removing 50 from 100) either way, final ans 50.
A simpler way to do this is to think of it from the right hand persons perspective, since the people we remove are only left handed, the 1 right handed person is constant, and therefore the percentage value they hold can help in calculating the rest, 1 is currently 1% of the total number of people, and since we need left handed people to become 98%, the remaining 2 % is the 1 Right handed person. So 1 went from being 1% of 100 to 2% of x. From there, it's straight forward. x*2/100=1. x=100/2=50. so the total number of people remaining in the room is 50, subtract that from the original number and you have the number of people that needs to be removed in order to match the required percentages.
50 Number of left handed people = x Number of right handed people = 1 Total number of people = x+1 x / x+1 = 0.98 x = 0.98*(x+1) x = 0.98x + 0.98 0.02x = 0.98 0.98/0.02 = x 49 = x
50. Basically the single right handed person is 1/100. For it to become 2/100 = 1/50, the number of left handed must decrease to 50-1=49. So from 99 to 49 is 50 left handed people must leave.
I did that 1% is represented as 1/100 (per-cent, as in per every one hundred) and you want 2/100. But you only have one singular right handed person so you have to do 1/50. 100-50 is 50 people. For reference, I am 13 years old and majority of my middle school class got it right. This is a middle school question, but not all adults remember such practice.
I still haven't watched the video nor read the comments, this is how I did it: 98% = (99-x)/(100-x), which yields x = 50. My explanation for the equation is the following. "99-x" is the final number of left-handed people in the room, x is the number of lefties who left (pun intended. Laugh!). The denominator will simply be the total number of of people in the room, which is one more than "99-x", so "100-x". Now, simply equals that with 98% and solve for x. By the way, the addition of one more comes about because there is a right-handed, airhead strolling about this weird left-handed people congress. Edit: yep! 👍🏻
I know dividing by 0.02 is mathematically correct, but very few people connect the dots and realise its same as multiplying by 50... next time it would be better say: 0.02 if you multiply by 5 you get 0.1 and if you multiply by another 10 you get 1 so lets multiply both sides by 50. Its easier to understand where the number came from OR rewrite it like 2/100 and multiply by its inverse 100/2. I have math as my hobby and while i understand some calculus lvl math I struggle sometimes.. mainly with proofs but also with some complex number problems and with "curve?" integrals (not native english speaker). Thanks for your videos and effort to make more people interested in math.
I’m not a smart person at all; but using the little knowledge I retained from high-school, I just mapped it in a basic graph. 1:1 gives you 50% equity (98 lefts need to leave). From the right perspective, you need approximately half that amount of people to leave (49). Then I realised 1/50 is 2%, so 50 had to leave.
50, 1 right handed, to double that, half the people need to leave After finishing the video: There are 2 simpler ways at looking at this problem. 1 & 99, what do we need to do to make 100 people = 98%, we simply replace 1 lefty with a righty, 2 & 98, and now, we can just remove half, 1R and 49L to maintain the ratio, or 50 people. The other way is as above. We want to make 1% become 2%, since we are doubling, we need to halve. I think these concepts are a little more intuitive, and easier to grasp. I wouldn't be surprised if even mathematicians spit out the wrong answer, or had to give it a bit more thought directly because they didn't look at the 1%, and instead focused on the 99%.
Like I mean if the question went Like this In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 97%?
@@kingellsgaming Not without cutting people in pieces. 3/100 equals 1 out of 33 1/3. So impossible 66 2/3 persons leaves the room. I don´t like that so let us take 96% as an new example. 4% rigthhanded is one out of 25. 75 lefthanded have to leave the room. I think you got it.
I did figure this out with algebra myself (proud me moment)! But then I decided to take it further and see what it would be for 97% and 96% and so on. As might be expected, only certain percentages work for whole numbers where in the difference from the total is just 1. As a matter of fact, there are only 7 ratios that work! They are the following: 99/100=99% 49/50=98% 24/25=96% 19/20=95% 9/10=90% 4/5=80% 1/2=50%
For me, the best mental method would be to think of the right handed (1) and put it as a constante, so to have 98% of left handed it means that 2% = 1, 100% = 2*50% => 2*x=98 => x=49 Then u know the total ammount of left handed guy and the original ammount so its easy
What’s crazier is in order to get down to 97%, you’d have to remove sixteen and two thirds more left-handers from the room. To get down to 96%, you’d then have to remove eight and a third more left-handers. To decrease by 1% each time, the total people who STAY in the room must go from 100 to 50 to 33.33 to 25 to 20 to 16.66 to 14.285714 etc. Notice this follows the pattern of denominators 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 etc. The number of people who need to LEAVE the room goes from 50 to 16.66 to 8.33 to 5 to 3.33 to 2.380952 to 1.7857142 etc. which follows a different pattern of denominators 1/(1x2), 1/(2x3), 1/(3x4), 1/(4x5), 1/(5x6), 1/(6x7) etc.
Because we are dealing with strictly whole numbers here, there are only a two ways a group of 100 or less can contain a subgroup comprising EXACTLY 98%. Namely, 98/100 or 49/50. The first is precluded since we start with 99/100 and we can't get to 98/100 by removing. So the second is the only outcome that fills the requirement: the number of lefties must go down by 50, leaving the original righty.
This isn't a particularly tricky question. What number is 1, 2% of? The answer is 50. So if you start of with 99 left handed people and 1 right handed person, you need to get rid of 50 lefties so you have 49 lefties and 1 righty left.
Nice seeing it all done out thoroughly. My thought process just went "if we only have 1 righty, what number is one 2% of? Yep, 50, get rid of 50 lefties".
To get 98% of something just divide 98/100 by 2, 49/50. Which is 98% in both cases, you can half it again, 24.5/25 which is 98% (one right side human and one left side. And yes they are different people which both have their dominant hand still. I could say it's the same person that is ambidextrous but that may not count)
For some reason this question was easy for me (which definitely isn't always the case with these math problems). But understanding percentages is hard for many people and maybe that's why this question causes problems. Great question/problem though 😊.
I got if from the right handed people. Right handed = 1%. When left handed = 98%, then right handed = 2%. Right handed number does not change, so when does 2% = 1 person. It's when the total is 50. That means 49 left handed people = 98%. 99-49 = 50 left handed people have to leave.
The first thing to do is just go the brute force route and see what % will be at some nice number that you can easily multiply into 100. Like 50, which just turns out to be the answer. Or you can understand that you have 1% and need 2%, thus you need twice more, which means that you need to divide the total by two without decreasing your 1%, thus you need 50 left-handed people to leave.
Each time a left handed person leaves, it changes the ratio of the group to the whole For exactly 98%, 50 would have to leave. 49/50 = 0.98 If we're rounding, between 34 and 60 would need to leave. 65/66 = 0.984 39/40 = 0.975 I'm presuming the first answer is the one the show wanted.
I knew it was a trick question but my immediate answer was also 1. Took me around half a minute to see the trick. So i thought then its has to be 99 left to 1 left, and since odd number wont give a whole %, it must be an even number. Then i started counting downwards, then realized half of 100 is 50 and half of 98 is 49. Lol thats how i ended up with 50.
I always come at these by solving for the total first, and the difference second. If we want 98% left handed, then we want to know 100% - 98% = 2% of some number = 1, so solve 0.02*x=1, to find that the new total number of people is 50 (1 right, 49 left). Then subtract, 99 - 49 = 50.
Easier way to calculate this: work with the fact that the number of right-handed people in the room (1) must be 2% in the final situation. If y is the total number of people in the room in the final situation, and 1 person equals 2% then y = 50. (1/y = 2% = 2/100 = 1/50 --> y = 50) And the number of left-handed people must be 50 - 1 = 49. So from the original 99 left-handed people, 50 have to leave.
Prompted by this puzzle, I mused on my percentage correct WORDLES and how many years of 100% correct wordles are required to inprove from 98% to 99%. Ive played 871 games so will need a string of 871 correct attempts to get to 99%. About 2 years 21 weeks without a single error, daunting!
Please help me solve this question. If A and ẞ are the roots of the equation x²+60^1/4x+a=0 such that A⁴+ẞ⁴= -30 then, find the product of all the real values of a.
We have the quadratic equation x²+(60^(1/4))x+a=0 with roots A and ẞ, it can be factorized as (x-A)(x-ẞ)=0, by expanding we get x²-(A+ẞ)x+Aẞ=0, therefore A+ẞ=-60^(1/4) and Aẞ=a. It is given that A⁴+ẞ⁴=-30 and we can also find that (A+ẞ)²=60^(1/2) and therefore A²+ẞ²=60^(1/2)-2a. Finally from A+ẞ=-60^(1/4) we get that (A+ẞ)⁴=60 and by expanding A⁴+4A³ẞ+6A²ẞ²+4Aẞ³+ẞ⁴=60 and (A⁴+ẞ⁴)+4Aẞ(A²+ẞ²)+6A²ẞ²=60, by substituting and reordering we get a²-2(60^(1/2))a+45=0, with roots a=60^(1/2)±15^(1/2), therefore the product is (60^(1/2)+15^(1/2))(60^(1/2)-15^(1/2))=45.
Great work! But solution seems less intuitive than it could be tbh (to my brain at least) You have initially 100 people. 99 left handed (called L) and one right handed (R) It is given that L/(L+R) = 0.99 No right handed will leave the room so lets set R to 1 Solve for L/(L+1) = 0.98 The solution is 49, you need 49 left handed people when you have 1 right handed in the room to get 98%. Which means 50 Left handed people have to leave.
If this were a question from a TV show, the participant likely would not have had enough time to solve the equation as Steve demonstrated. Perhaps we can think of it this way: The percentage calculation in the question is always in the form of (x-1)/x, where x is the total number of people left in the room. The required percentage, 98%, can be expressed as 98/100=49/50, which matches the form (50−1)/50.
Another intuitive way to think of this is to change the side you're looking at. If only 1% are right handed, we need to get that to 2% in order to reduce the left handed side to 98%. We can't double the number of right handed people to reach that target since we're only allowed to remove people, so we have to reduce the number of left handed people by 50%
I'm 43 years old and this is the first time i've seen a useful implementation of something that i forgot in the last millenium. But the fact, that one person equals 2% in 50 people was just an intuitive thought at start of the video 😅
I just did it by rule of 3. *No matter how many left handed leave, the number of non-left handed stays 1. That means 1 will be 2% of the total.* *1 --- 2 ; x --- 98 -> 1/x = 2/98 -> 2x = 98 -> x = 49* So 49 is the number of left-handed remaining, and 99 the number before they leave. 99 - 49 = 50 left handed people leave.
The asnwer is simple 50 That way you have 49 peft handed people and 1 right handed person. Which is 2% right handed. But at first glance it does trick you.
I initially thought the answer was 1, but then realised that then goes from 1 right handed in a hundred to 1 in 99 which does not equate to 98%. Then I realised you need one person to be 2% of the room which means there needs to be 50 people, of which one is right handed. So to go from 100 to 50, then 50 must leave.
I thought 1 at first but then realized that only works if a right-handed person comes in to replace them. Did the work and I got 50 people needed to leave to get 98% left-handed people. (99-x)/(99-x)+1 = .98 99-x = (.98)(99-x+1) 99-x = 97.02-.98x + .98 99-x = 98-.98x 1 = 0.02x 50 = x
1 ÷ 0 = 0? (a 3rd grade teacher & principal both got it wrong), Reddit r/NoStupidQuestions
ua-cam.com/video/WI_qPBQhJSM/v-deo.html
Undefined, but it approaches infinity. So, 0 is about as wrong an answer as you can get.
@@TommyBo42 Not "but it approaches infinity".
Instead, "something" approaches infinity.
That something is actually "something else" ppl dont understand unless they have knowledge of math analysis.
@@TommyBo42 no
if f(x)=1/x .. as x increases or approaches infinity f(x) gets smaller
..if x goes towads zero f(x) increases
.. but f(x)is Undefined for x=0
..it makes as much sense as take the Inverse sine of 2 wich is undefined
Hence, my answer that it is undefined, but it approaches infinity as x gets closer to zero :) Cheers!
初探討極限理論? 相當嗨~
其實學好一點數學, 也沒什麼.
I thought about it like this. At the beginning there is one right-handed person in the room. How many left-handed people do I need for there to be 2% right-handed people in the room? Clearly I need 49. Therefore I have to remove 50 left-handed people. I did all this in about 5 seconds.
yeah, it's easiest and fastest to turn the percentage of right-handed people into a ratio to all people in the room. I thought about it about the same: 1% is 1:100, and then 2% is 2:100, or 1:50. to get from 1:100 to 1:50, you take away 50 left-handed people.
yeah, this is the obvious way to do it and shows that logic beats algebra in speed
@@eventhorizon853speed is not the reason you use algebra. It’s because of its reliability and verifiability.
Yeah very clickbait
yes
50 people. That stumped me for a hot minute before i realized what happens when you remove a person.
The bouncer will have had a full day!
I knew it wasn't 1 person but I didn't expect 50 .😂
But 49/50 will get you 98%.
I realized immediately that just removing a person would result in a non-integer percentage, but it took me a while to realize what else to do. But I'm proud to say I got the answer before he said it!!!
ya, took a min realise what was asked...
but its easier calculate on those right handed
u want right handed to be 2% ot the total left in the room ->
1/.02=50 ppl must be left in the room
..would had been fun if thay asked how many have to leave to bring it down to 97%
From memory: _this is one of those where it's about half isn't it?_
I'm glad to see that a lot of people didn't go through the entire process, and rather know or have come to the conclusion that in order to double the percentage of right-handed people, you need to halve the total number.
Hello. I've only began to pursue math recently after a long break since the end of school. This problem did not come intuitively at all for me, do you have anything you would recommend beside doing more of these, or is it just a natural talent I don't have?
@@TroySturges-g6u make excel spreadsheets about video games with respect to crit chance, crit damage, attack speed, damage mitigation, effective total health etc. You'll get intuitive about percentages real quick
@deesire thank you for your reply, I will give it a go!
That is going through the entire process, only very quickly. When you solve in your head, you go through all the steps, just without spending so much time writing.
The small change from 99 to 98 obscures the large relative change from 1 to 2. This is a good general lesson.
That is a superb analysis from you there.
The quiz show that this question is from i was watching when aired, i was furious that i got it wrong, but your lesson there im gunna remember for future maths questions.
I thought about it like this:
When you want 100 people with 98% left handed, you need 98 left handed and 2 right handed people.
Then I divided both by two so there’s only one right handed person. That left me with 49 left handed people.
And 99-49=50, so 50 left handed people have to leave.
Yes! And this is so much easier
@@TrentRProductions Lol, I was reading the comments while assuming the video gave the quick solution. But now I took a look at the video and it is truly horrible, lol.
That's clever
I calculated it using some algebra. The original percentage of 99% is 99 left-handed people out of 100 people in total.
If we represent the number of left-handed people that will leave the room with “x”, then we have (99 - x)/(100 - x) = 98% (the new percentage we are looking for) = 0.98.
Once you work it out, you get x = 50.
@@ronald3836now tell me how many people need to leave for the percentage to be below 93.5%. You can’t do that just by looking at it but the formula still holds up. Maybe think for a second why what he is doing might be important
I found it easier leaving the percentage as a fraction:
(99-x)/(100-x) = 98/100
100(99-x) = 98(100-x) (distribute denominators)
9900 - 100x = 9800 - 98x
98x - 100x = 9800 - 9900
-2x = -100
x = 50
don't even need all that. 2% is 1/50th of total. so 50 people need to leave
@@bytemeahyou DO need all that to work it out in a formal and logical fashion that others can follow and learn from. Shortcuts don’t do that.
Man thanks so much
It is much easier 🎉🎉
The Percentile quantities were Supposed to Confuse the Reader, as some commenters STATED, it's Best to make a Formal Computation rather than Follow a Seemingly Logical answer...😊😎👍
Much easier to understand
Go in the opposite direction: start with 1 right-handed person. How many lefties do you need to bring in to the room to get to a ratio of 100:2 (given that the max number of righties is 1)?
Percentage = x/ (x+1), set percentage to 98/100 which is = to 49/50=x/(x+1), x ist equal to 49. So 50 left handed ppl had to leave since 99-50 is 49
I couldnt remember the percentage formulas so couldnt do it in the time alloted, 40 years ago maybe
The multi marker skills are impressive
Yes, I noticed that in another of his videos.
How many markers can he multiplex ...maybe 5 ? :)
he is a true master of the ancient Black Pen Red Pen Technique 🖍️
@@LonkinPork 2 pens, 1 guy
@@Not.Your.Business reminds me of 1 cup 2....
This is the first one on your videos that I figured out immediately. My brain went to one person is 1% in the initial scenario, so for someone to be 2% of the group there would need to be half the total people.
That's a brilliant way of thinking about it.
Me too. I'm much too lazy to do the math when there is an easier way to come up with the answer.
That’s how I did it as well.
It feels good to be a part of that 1% club
The club of 1% righthanded people in the room?!?
@@JuergenW. the concept of the original show is the questions get harder based on how many people are able to answer them, and the final question is supposed to be answerable only by 1% of people. They have a panel of 100 people answering the questions along with the contestant and you see how many of them go out on each question.
Of course, it doesn't mean the same 1% will be able to answer all of the 1% questions on the show. Some, like this one, I find quite easy. Others are more complicated.
No need to guess. Just reason how many people you need to have the sole right-handed person represent 2%.
2% means 1 out of 50. That's all.
5:00 fifty!
This assumes you don't remove the one right-handed person! Then, it suddenly becomes (and remains) 100% left-handed.
@@jamesharmon4994
The original problem says ‘how many left-handed people have to leave the room’.
@jamesharmon4994 the questions specifies left handers
Instead of leaving the room just make them ambidextrous and then slowly phase out their left hand
@Kerguelen.Mapping Then... you just have to do it to ONE person.
Thanks for the Christmas gift of allowing us to momentarily feel smart.
50. Had to pull out a calculator and guess-and-check. Never would have been able to figure that out on the spot on a gameshow.
Yeah with a lot of money riding on the answer - no pressure!
Had to quickly do it in my head. So, I'm pretty sure I would have got it.
04:47 It would be easier to calculate this, if we would firstly multiply both sides by 100 (to get 100=2*x), and secondly divide both sides by 2 (to get 100/2 = x and x=50).
I used a slightly different method.
99 are left handed so that means 1 is right handed. 1 out of 100 equals 1%
1 out of 50 total equals 2%. That means 50 less Total people.
Wow that’s really smart. I feel like that observation is the fastest method possible.
we use the same method what a coincidence
Very nice demonstration. I went the other way. The number of rightanded is constant, always 1. If 98% are lefthanded then 2% are right handed. The total number of people to have 1 person be 2% is 2/100=1/x -> 2=100/x -> 2x=100 -> x=50. W started with 100 people, so (100-50) = 50 has to leave.
50. It’s a simple equation (99-x)/(100-x) = 0.98 . Which simplifies to 0.02x = 1 and hence x=50
1 in a 100 (1+ 99 (%)) must go to 2 in a 100 (2 + 98(%)). But we had only 1 righthanded, so 2 and 98 divided by two (in order to get 1 righthander), leaves 49 lefthanders. We had 99 lefthanders, so 50 have to go...😊
Out of interest I asked ChatGPT and it told me the answer was 1, the right-handed person had to leave the room lol
Chat gpt o1 respondeu corretamente.
Thats chat gpt for you, cant even do what computers are supposed to be good at 🤣 i cant belive people want that thing to be npc dialogue for games
I asked chat Gpt and it gave the correct answer with calculations
@@utopiandystopia1383Maybe you are not using Gpt 4o I tried it multiple times and it gave the right answer
As others have pointed out, I solved it by thinking how many people in total they had to be for one person to equal 2%, which is one out of fifty (so 49 others). Thus simply 99-50 = 49. But I appreciate the more algebraic solution to the general problem, where the numbers might be harder to think about in your head.
I figured it'd be an easy enough question to do without calculator or pen and paper, so I simplified 98/100 and got the answer pretty quickly.
The solution in the video seems sooo complicated almost as if you were searching for the most complex way possible
The most straightforward and obvious solution for me is to realize this:
We have one person which makes 1% of the total amount of group.
1/0,01 = 100
Now, that same one person should make 2% which means:
1/0,02 = 50
That's it. No more complications with equations or anything
In chemistry, if you want to double concentration - you should somehow halve mass or volume. 😉
Same thing indeed.
Was afraid this could become a bloody affair, but al well ends well 😄! The explanation is a bit beyond the obvious, love it
The gameshow gives you 30 seconds to solve, took me about 15 when I realized 98/99 is still pretty close to 99%... and a short jump to 49/50 is 98%.
Yes! I got it after looking at the thumbnail and just thinking about it for half a minute! A bit pleased by myself now..😅
(Ans:50)
Quick intuitive approach - equation balancing, you want to double the number of right handed people, inversely, you need to half the number of left handed.
You need to halve the total number of people in the room! Your stated approach 99/2=49.5 is a bit brutal and doesn't solve the problem!
( Not questioning your reasoning, you didn't word it right! )
@alexandergutfeldt1144 correct, I didn't want to write an essay. I left out the parts of keeping the total number of people at 100 by converting the lefts to rights, reducing by the desired ratio (accidental time stamp), then converting back with the new group. Thanks for keeping me honest, I lazy math often.
@@alexandergutfeldt1144 are you stoo-pid ??
He clearly wrote "quick INTUITIVE approach"
He didn't write "correct calculation"
Do you ever get invited to social events?
i just watched 10 times how you switched your pens 1:03 ... awesome! and great content!
Another problem is asking how to bring the percentage down to 96%. The answer is 75 left-handed people must leave the room leaving 1 right-handed person and 24 left-handed people. 24 out of 25 is 96%. The easier way to calculate this is to concentrate on the number of right-handed persons which is always one. 1=4x/100 which equals 25 so there are 24 left-handed and 1 right-handed so 75 of 99 left-handed must leave the room. In the problem given the equation would be 1=2x/100 which equals 50 so there is 1 right-handed and 49 left-handed (49 out of 50 is 98%) so 50 left-handed must leave the room. This math is easier than what is shown.
Took me ages to realize if people leave there would no longer be 100 people... Once this was clear, answer became obvious.
In a TV show I would have panicked.
Bro how lucky am I to search this and only your video came up that was uploaded 5hr ago. Nice
Answer should. Be 50 ..
Initially we have 99 left handed person and 01 right handed person .. in the scenario we did not change no. Of right handed person that is 01 according to required condition 01 should be 2% of total persons in the room so 49 person will be 98% sir that 50 person have to left eoom
This is a great question to ask LLMs. They have lots of trouble with it...
Nah they solve it without problem
I read the thumbnail and immediately started guessing n/(n+1) values until I found the answer, then I started the video. The algebraic method and logic makes a lot of sense!
I solved it mentally with algebra. The hardest part was remembering the numbers, keeping them in mind. Here ‘s the equation: 99-x/ 100-x = 98/100. It took me more than 30 seconds to do it, though. Still, not bad for an octogenarian!
Another easier calculation is to look at fixed values. Number of right-handed is 1, we need to increase from 1% to 2%
1/(100-x) = 2/100
x=50
Let us assume that x people have to leave.
So, if 99/100 x 100 = 99%, then
100(99-x)/100-x = 98%
9900 - 100x = 9800 - 98x
100 = 2x
50 = x
U're wrong
Easier to look at the number who can stay. 2% means 1 in 50. So 50 stay, therefore 50 leave.
@@kotbegemot9177It'd be more helpful if u explain what's wrong instead of just saying it
@@ronald3836I wrote as how you would write in an exam or if you are bad with mental calculations
@@leaDR356 i mean that, "98%" should be "0,98" in your calculation, equation
If 98% are left-handed, then 2% must be right-handed.
2. In the room, there’s only 1 right-handed person, and that 1 person represents 2% of the total number of people after some have left.
3. To figure out the total number of people, you ask:
• “What total number of people makes 1 equal 2%?”
• The answer is: 100% ÷ 2% = 100 ÷ 2 = 50.
50 people, 99/100 is 99% 49/50 is 98% Kevin of Vsauce2 covered this exact thing albeit with a different premise (something to do with potatoes iirc). You can also look at it the other way round, there is 1 right handed person 1 out of 100 is 1% you need it to be 2% so 1/0.02 (or 100/2) which is 1 out of 50
I see this proportion on a screen is the proper way, but I solved it like that:
Basically: 100 = 100*0.98 + r (r - the number of right-handed people, we know it's 1 very easily, but for the sake of demonstration)
And in the new case: N = N*0.98 + R (N - the new total number of people, new R just for the demo)
At the same time: N = 100 - Ld + R (Ld - the lefties number difference from the original 100)
So we substitute: 100 - Ld + R = (100 - Ld + R)*0.98 + R
100 - Ld = 98 - 0.98Ld + 0.98R
2 - 0.98R = 0.02Ld (we know R = 1 though, otherwise no go)
1.02 = 0.02Ld
Ld = 51 - number of lefties should leave, so overall it will be 50 people
Easier mathematical manipulation if you recast as right-handed percentage. 1 right-handed person in the room with 99 left-handed is 99% left handed or 1% right handed. So to go down to 98%-left is to go up to 2%-right. Equation is almost the same but much quicker to solve since there is always 1 right handed peron and "x" left-handed people need to leave ther room
1/(100-x) = 0.02 Note it is easier if you recall that 0.02 = 2/100 = 1/50
1/(100-x) = 1/50 So 100-x = 50. x=50
to try to solve it within 30 seconds
a viable option is
98% = 98/100
reduce this fraction
49/50
luckily the original condition was 99/100 = 99%
so removing 50 from numerator and denominator (removing 50 left handed people removes 50 from total)
leads to 98%
looking at the comments, the 1% to 2% trick is even better (thinking of the complement, amount of right handed people)
1/100
2/100 = 1/50 (so removing 50 from 100)
either way, final ans 50.
I like your method, too.
A simpler way to do this is to think of it from the right hand persons perspective, since the people we remove are only left handed, the 1 right handed person is constant, and therefore the percentage value they hold can help in calculating the rest, 1 is currently 1% of the total number of people, and since we need left handed people to become 98%, the remaining 2 % is the 1 Right handed person. So 1 went from being 1% of 100 to 2% of x. From there, it's straight forward. x*2/100=1. x=100/2=50. so the total number of people remaining in the room is 50, subtract that from the original number and you have the number of people that needs to be removed in order to match the required percentages.
Better method to solve that algebra -
(99-x) / (100-x) = 98/100
Add and subtract 1 from 99 - x
(100-x-1) / (100-x) = 98/100
[(100-x) / (100-x)] - [1/(100-x)] = 98/100
1 - 1/(100-x) = 98/100
1 - 98/100 = 1/(100-x)
(100-98)/100 = 1/(100-x)
2/100 = 1/(100-x)
1/50 = 1/(100-x)
50 = 100-x
x = 100-50 = 50 Ans.
50
Number of left handed people = x
Number of right handed people = 1
Total number of people = x+1
x / x+1 = 0.98
x = 0.98*(x+1)
x = 0.98x + 0.98
0.02x = 0.98
0.98/0.02 = x
49 = x
I solved it in 10 seconds:
If they are 100 people every person is 1%, half of those and every person equals 2% so they need to be 49 out of 50.
Same here, same reasoning, about the same time!!
Yep, but you didn’t prove it. That’s what this video is about. Finding the solution is not hard at all. Proving it is something else. Gratz though 🎉
I solved in too in a couple of seconds! I skipped the video to the end :-D
Bro, your channel is the best. :)
50. Basically the single right handed person is 1/100. For it to become 2/100 = 1/50, the number of left handed must decrease to 50-1=49. So from 99 to 49 is 50 left handed people must leave.
I did that 1% is represented as 1/100 (per-cent, as in per every one hundred) and you want 2/100. But you only have one singular right handed person so you have to do 1/50. 100-50 is 50 people. For reference, I am 13 years old and majority of my middle school class got it right. This is a middle school question, but not all adults remember such practice.
I still haven't watched the video nor read the comments, this is how I did it:
98% = (99-x)/(100-x), which yields x = 50.
My explanation for the equation is the following. "99-x" is the final number of left-handed people in the room, x is the number of lefties who left (pun intended. Laugh!). The denominator will simply be the total number of of people in the room, which is one more than "99-x", so "100-x". Now, simply equals that with 98% and solve for x.
By the way, the addition of one more comes about because there is a right-handed, airhead strolling about this weird left-handed people congress.
Edit: yep! 👍🏻
I know dividing by 0.02 is mathematically correct, but very few people connect the dots and realise its same as multiplying by 50... next time it would be better say: 0.02 if you multiply by 5 you get 0.1 and if you multiply by another 10 you get 1 so lets multiply both sides by 50. Its easier to understand where the number came from OR rewrite it like 2/100 and multiply by its inverse 100/2. I have math as my hobby and while i understand some calculus lvl math I struggle sometimes.. mainly with proofs but also with some complex number problems and with "curve?" integrals (not native english speaker). Thanks for your videos and effort to make more people interested in math.
99 out of 100 (initial)
98 out of 100 (final)
Final one can be written as 49 out of 50 tooo so basically u took out 50 people.
I’m not a smart person at all; but using the little knowledge I retained from high-school, I just mapped it in a basic graph. 1:1 gives you 50% equity (98 lefts need to leave). From the right perspective, you need approximately half that amount of people to leave (49). Then I realised 1/50 is 2%, so 50 had to leave.
What I did was the "what if the roles were flipped" case and continued until 0.9^(100-x) >= 0.01, which gave me an answer of... 55!
50, 1 right handed, to double that, half the people need to leave
After finishing the video:
There are 2 simpler ways at looking at this problem.
1 & 99, what do we need to do to make 100 people = 98%, we simply replace 1 lefty with a righty, 2 & 98, and now, we can just remove half, 1R and 49L to maintain the ratio, or 50 people.
The other way is as above.
We want to make 1% become 2%, since we are doubling, we need to halve.
I think these concepts are a little more intuitive, and easier to grasp.
I wouldn't be surprised if even mathematicians spit out the wrong answer, or had to give it a bit more thought directly because they didn't look at the 1%, and instead focused on the 99%.
Only one person right handed. 2% right-handed = 1/50 so 50 left-handed have to leave the room.
Exactly.
How did u get 2% please I'm so confused. Help me
Wait I got how u got that now so is it also applicable if what I need to remove is 3%?
Like I mean if the question went Like this
In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 97%?
@@kingellsgaming Not without cutting people in pieces. 3/100 equals 1 out of
33 1/3. So impossible 66 2/3 persons leaves the room. I don´t like that so let us take 96% as an new example. 4% rigthhanded is one out of 25. 75 lefthanded have to leave the room. I think you got it.
Pre watch guess
50 because then it would be 49/50 which is 98/100
The Righty is 1% of the 100. To reach 2% (98% Lefty) the total must half. I like the algebra approach also.
I did figure this out with algebra myself (proud me moment)! But then I decided to take it further and see what it would be for 97% and 96% and so on. As might be expected, only certain percentages work for whole numbers where in the difference from the total is just 1. As a matter of fact, there are only 7 ratios that work! They are the following:
99/100=99%
49/50=98%
24/25=96%
19/20=95%
9/10=90%
4/5=80%
1/2=50%
My answer before watching the video was 0.5, I was almost there! 🤣🤣🤣
For me, the best mental method would be to think of the right handed (1) and put it as a constante, so to have 98% of left handed it means that 2% = 1, 100% = 2*50% => 2*x=98 => x=49
Then u know the total ammount of left handed guy and the original ammount so its easy
What’s crazier is in order to get down to 97%, you’d have to remove sixteen and two thirds more left-handers from the room. To get down to 96%, you’d then have to remove eight and a third more left-handers. To decrease by 1% each time, the total people who STAY in the room must go from 100 to 50 to 33.33 to 25 to 20 to 16.66 to 14.285714 etc. Notice this follows the pattern of denominators 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 etc.
The number of people who need to LEAVE the room goes from 50 to 16.66 to 8.33 to 5 to 3.33 to 2.380952 to 1.7857142 etc. which follows a different pattern of denominators 1/(1x2), 1/(2x3), 1/(3x4), 1/(4x5), 1/(5x6), 1/(6x7) etc.
I was given a similar question years ago in high school, and yeah, it stumped me. However, that's one of those things that only gets you once!
Because we are dealing with strictly whole numbers here, there are only a two ways a group of 100 or less can contain a subgroup comprising EXACTLY 98%. Namely, 98/100 or 49/50. The first is precluded since we start with 99/100 and we can't get to 98/100 by removing. So the second is the only outcome that fills the requirement: the number of lefties must go down by 50, leaving the original righty.
This isn't a particularly tricky question. What number is 1, 2% of? The answer is 50. So if you start of with 99 left handed people and 1 right handed person, you need to get rid of 50 lefties so you have 49 lefties and 1 righty left.
Very simple
(99-x)/(100-x)=98%
x=50
Since headcount is a scalar value thus only non-negative real numbers have to be concerned.
It is just so easy.
Nice seeing it all done out thoroughly.
My thought process just went "if we only have 1 righty, what number is one 2% of? Yep, 50, get rid of 50 lefties".
Much simpler: If x is the number that (approximates or) gives a 98% ratio: x/x+1 =98/100 reduces to x=49 ie 99-50
To get 98% of something just divide 98/100 by 2, 49/50. Which is 98% in both cases, you can half it again, 24.5/25 which is 98% (one right side human and one left side. And yes they are different people which both have their dominant hand still. I could say it's the same person that is ambidextrous but that may not count)
Glad I'm still smort enough to solve this😂
For some reason this question was easy for me (which definitely isn't always the case with these math problems). But understanding percentages is hard for many people and maybe that's why this question causes problems. Great question/problem though 😊.
I got if from the right handed people. Right handed = 1%. When left handed = 98%, then right handed = 2%. Right handed number does not change, so when does 2% = 1 person. It's when the total is 50. That means 49 left handed people = 98%. 99-49 = 50 left handed people have to leave.
The first thing to do is just go the brute force route and see what % will be at some nice number that you can easily multiply into 100. Like 50, which just turns out to be the answer. Or you can understand that you have 1% and need 2%, thus you need twice more, which means that you need to divide the total by two without decreasing your 1%, thus you need 50 left-handed people to leave.
I love your videos! I’m terrible at math, yet I find so many elements about it (like this) so truly fascinating.
Took me about 10 seconds of thinking to come to the right solution.
Each time a left handed person leaves, it changes the ratio of the group to the whole
For exactly 98%, 50 would have to leave. 49/50 = 0.98
If we're rounding, between 34 and 60 would need to leave. 65/66 = 0.984 39/40 = 0.975
I'm presuming the first answer is the one the show wanted.
I knew it was a trick question but my immediate answer was also 1. Took me around half a minute to see the trick. So i thought then its has to be 99 left to 1 left, and since odd number wont give a whole %, it must be an even number. Then i started counting downwards, then realized half of 100 is 50 and half of 98 is 49. Lol thats how i ended up with 50.
I always come at these by solving for the total first, and the difference second.
If we want 98% left handed, then we want to know 100% - 98% = 2% of some number = 1, so solve 0.02*x=1, to find that the new total number of people is 50 (1 right, 49 left). Then subtract, 99 - 49 = 50.
Easier way to calculate this: work with the fact that the number of right-handed people in the room (1) must be 2% in the final situation. If y is the total number of people in the room in the final situation, and 1 person equals 2% then y = 50.
(1/y = 2% = 2/100 = 1/50 --> y = 50)
And the number of left-handed people must be 50 - 1 = 49. So from the original 99 left-handed people, 50 have to leave.
One of these problems that's good to start solving "backwards", i.e. let's notice that 98% = 49/50 😉
99-x = 49
100-x = 50
x = 50
Prompted by this puzzle, I mused on my percentage correct WORDLES and how many years of 100% correct wordles are required to inprove from 98% to 99%. Ive played 871 games so will need a string of 871 correct attempts to get to 99%. About 2 years 21 weeks without a single error, daunting!
Please help me solve this question.
If A and ẞ are the roots of the equation x²+60^1/4x+a=0 such that A⁴+ẞ⁴= -30 then, find the product of all the real values of a.
We have the quadratic equation x²+(60^(1/4))x+a=0 with roots A and ẞ, it can be factorized as (x-A)(x-ẞ)=0, by expanding we get x²-(A+ẞ)x+Aẞ=0, therefore A+ẞ=-60^(1/4) and Aẞ=a. It is given that A⁴+ẞ⁴=-30 and we can also find that (A+ẞ)²=60^(1/2) and therefore A²+ẞ²=60^(1/2)-2a. Finally from A+ẞ=-60^(1/4) we get that (A+ẞ)⁴=60 and by expanding A⁴+4A³ẞ+6A²ẞ²+4Aẞ³+ẞ⁴=60 and (A⁴+ẞ⁴)+4Aẞ(A²+ẞ²)+6A²ẞ²=60, by substituting and reordering we get a²-2(60^(1/2))a+45=0, with roots a=60^(1/2)±15^(1/2), therefore the product is (60^(1/2)+15^(1/2))(60^(1/2)-15^(1/2))=45.
@@Mushishi-hz6mtWhy (A+B)²= 60^(1/2) not -60^(1/2)
Since A+ẞ=-60^(1/4), by squaring both sides we get (A+ẞ)²=(-60^(1/4))²=60^(2/4)=60^(1/2)
Nice algebraic work! Math is your friend!
Great work! But solution seems less intuitive than it could be tbh (to my brain at least)
You have initially 100 people. 99 left handed (called L) and one right handed (R)
It is given that
L/(L+R) = 0.99
No right handed will leave the room so lets set R to 1
Solve for
L/(L+1) = 0.98
The solution is 49, you need 49 left handed people when you have 1 right handed in the room to get 98%. Which means 50 Left handed people have to leave.
Answer is 50 ,you can easily solve it in 10 sec by making an equation .( 99-x/100-x) = (98/100).
I’m answering before watching 50. Used a calculator to confirm. Answer has to result in whole number percentage. IE: 49/50 =0.98
If this were a question from a TV show, the participant likely would not have had enough time to solve the equation as Steve demonstrated. Perhaps we can think of it this way:
The percentage calculation in the question is always in the form of (x-1)/x, where x is the total number of people left in the room. The required percentage, 98%, can be expressed as 98/100=49/50, which matches the form (50−1)/50.
My technique was to say, "watch it be something like 50." Worked like a charm. 😁
The trick was to not let intuition kick in and remember the definition of probability (favored cases)/(all possible cases)
Another intuitive way to think of this is to change the side you're looking at. If only 1% are right handed, we need to get that to 2% in order to reduce the left handed side to 98%.
We can't double the number of right handed people to reach that target since we're only allowed to remove people, so we have to reduce the number of left handed people by 50%
My thought process :
X × 2/100 = 1 (Right handed %age for 98% left handed people)
X = 100/2
Therefore, X = 50
I'm 43 years old and this is the first time i've seen a useful implementation of something that i forgot in the last millenium. But the fact, that one person equals 2% in 50 people was just an intuitive thought at start of the video 😅
I just did it by rule of 3. *No matter how many left handed leave, the number of non-left handed stays 1. That means 1 will be 2% of the total.*
*1 --- 2 ; x --- 98 -> 1/x = 2/98 -> 2x = 98 -> x = 49*
So 49 is the number of left-handed remaining, and 99 the number before they leave. 99 - 49 = 50 left handed people leave.
I did it as a fraction. 99+1 currently. Need 98/100, but people need to leave. Simplify. 98/100= 49/50, so 50 need to leave to have 49+1
The asnwer is simple 50
That way you have 49 peft handed people and 1 right handed person. Which is 2% right handed.
But at first glance it does trick you.
I initially thought the answer was 1, but then realised that then goes from 1 right handed in a hundred to 1 in 99 which does not equate to 98%. Then I realised you need one person to be 2% of the room which means there needs to be 50 people, of which one is right handed. So to go from 100 to 50, then 50 must leave.
I thought 1 at first but then realized that only works if a right-handed person comes in to replace them. Did the work and I got 50 people needed to leave to get 98% left-handed people.
(99-x)/(99-x)+1 = .98
99-x = (.98)(99-x+1)
99-x = 97.02-.98x + .98
99-x = 98-.98x
1 = 0.02x
50 = x