The sum of two numbers is 188 and the difference is 34. What are the numbers?
Вставка
- Опубліковано 2 чер 2024
- How to solve an algebra linear system word problem.
TabletClass Math Academy
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
All Courses - TCMathAcademy.com/
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...
I just found half of 188 to be 94, 94 x 2 = 188, so I added half the difference given (i.e., 34) to one of those 94s and subtracted half the difference from the other. 94 + 17 = 111 and 94 - 17 = 77.
Yah that is what I did.
I'm glad I saw this reply...I was about ready to post the same thing! To prove you're right, 111+77=188. 111-77=34. If you're like me, it took only as many seconds to figure this out, as the number of minutes this video took to explain it!😎😎
I did in my head - subracted the 34 from 188, divided by 2 for first number, added the 34 for second - 77 & 111.
That’s ow I did it in my head also
I did it similarly dividing 188 by 2 to get 94, then dividing 34 by 2 and subtracting that from one of my 94s and adding it to the other. Your way is easier.
Beware in some exams there are marks for method so may well be wanting variable like x.
Would depend on the exam.
I did the exact same method. Easy peasy
That's so helpful more than video
I divided the 188 and got 94. I divided the 34 and got 17. I then added 17 to 94, getting 111. Then subtracted 111 from 188, getting 77.
I went that way too.
The same. Cool.that’s away of a thinking brain
Sheesh...an example of making an easy solution hard..
Nice mathematical reasoning!
Same. Kind of brute the answer. It worked for this one.
I solved using X + (X + 34) = 188. 2X = 188-34. 2X = 154. X=77. X+ 34 = 111
You know what you're doing, which is good. You're still working with two variables, but you've processed one of them in your head, rather than on paper. That makes it less easy for someone else to follow along. Better, I think, to be verbose and take small steps, rather than leaps.
Showing where the (X+34) came from would add clarity. You could start with the second equation and transpose so that y is isolated on the left side. Then show the substitution into the first equation.
Also, this part has combining terms, subtracting from both sides, and the result of that subtraction, all occurring in one step:
X + (X + 34) = 188. 2X = 188-34.
In my opinion, they should be done in separate steps so others can more clearly see what you're doing.
--------------------------------------------
[Difference]
Y - X = 34
Y - X + X = 34 + X
Y = 34 + X
Y = X + 34 ------------ (We'll use this now and at the end.)
[Sum]
X + Y = 188
(substitute)
X + (X + 34) = 188.
2X + 34 = 188
2X + 34 - 34 = 188 - 34
2X = 154
X = 77
Excellent explanation. I had a page of scribbled equations as I floundered around. Your solution revived my flagging brain in seconds! 👍
@retread1083
How about?
X + Y = 188
X - Y = 34
Add the two equations to get
2 × X = 222
X = 222 / 2 = 111
Y = X - 34 = 111 - 34 = 77
@@dougnettleton5326 That certainly gets to the correct values but if you don't mind, I'll offer some suggestions to improve your presentation. I think it adds clarity if you start a new line for each change, so I'd avoid stringing equalities across the same line. You could add a line when you solve for X to literally show the addition before actually performing the addition.
X + Y = 188
X - Y = 34
Add the two equations to get
X + Y + X - Y = 188 + 34
@retread1083
Very funny😂
My original solution was:
X + Y = 188
X - Y = 34
Add to eliminate Y
2X = 222
X = 111
Y = 111 - 34 = 77
The deleted stuff was added for clarity. I had a line at the end "No need to write a book" but deleted it.
I don't think anyone needing the painful level of detail you provided would be able to work a device where they would encounter the video with the problem.
I wish I had a teacher like you when I was in school! I've learned more by watching your videos than I learned in four years of high school. Thank you.
Same
Greetings. The numbers are 111 and 77. We determine the values as follows. We assume that the numbers are X and Y. Thereafter, the sum of these numbers will be ( X +Y) and since we are told that these numbers added is equal to 188, we have X +Y=188. The difference of these numbers equal 34, that is X-Y=34. Now we have two equations with the unknowns X and
Y. To determine the values for X and Y, we first eliminate one of the unknowns. We do this by adding the two equations to eliminate Y, that gives 2X = 222, and X = 111. To find the value of Y, we substitute the value for X in either equations. Using equation (2), X -Y = 34 gives
111-Y= 34 and -Y= 34 -111= 77. Lovely.
Devide the total (188) in half (188/2=94), subtract half of the difference (34) from 94 (94-17=77) and add half of the difference to 94 (94+17=111). The two numbers are 77 and 111.
I took a different route. I subtracted 34 from 188, leaving 154. Then I divided 154 by 2, giving me 77. Then I added the 34 to 77 to give me the other number, 111. The algebraic equation I used was X + 34 + X = 188, or 2X + 34 = 188, or 2X = 154, or X = 77, and X + 34 = 111.
Hey, whatever works for you. If everyone thought and processed things the same way, it'd be a boring world.@@TheHawk--oe8iq
The easiest technique is to halve 188 which gives you 94 then take away half of 34(17) from 94 which leaves 77. 188 - 77 is 111. Therefore 111 and 77 is your answer. Algebra not needed. Just common sense.
its far easier to just add 188 + 34 = 222 and then divide by 2 to get 111, which is the first number. For the other number you can either subtract 34 and you get 77 or you subtract the 111 from 188 to get 77.
The goal is to find the answer using the tool of algebra, your limitless powers put aside.
@@marcreider9573mine is using algebra, just a shortened form of it.
x + y = 188
x - y = 34
add both equations and you get
2x = 222 |:2
x = 111
then use that in one of the first equations to get the value of y = 77.
That was a fun one to figure out. X=111, Y=77. First I tried to reword it so there was only one variable. If X-Y=34, then X=Y+34. From that, you can use (Y+34) to substitute for X. X+Y=188 becomes (Y+34) + Y = 188. Or 2Y+34=188... 2Y=154 ... Y=154/2 ... Y=77. If X=Y+34, then X=111. I did it differently than John, but it works.
This is much easier than it sounds
We have two numbers to find .. but .. we can call them N and N + 34
and we know that N + N + 34 = 188
N + N = 188 - 34
2N = 154
N = 77 and the other number is 77 + 34 = 111
i just divided 188 by two in my head, and added half of 34 to it to get the first number. So, (188/2) + (34/2) = 111. Then either subtract 111 - 34 to get 77, or just go (188/2) - (34/2) = 77. Haven't watched the video to see how he did it, but watched far enough to check my answer.
While adding the equations works just as well, I was taught substitution. Solve the first equation for one variable and replace that variable in the second equation.
77 and 111. Simply just make two equations.
a + b = 188
b - a = 34
Use substitution to find b on one equation and plug it into the other.
b = 188 - a
(188 - a) - a = 34
188 - 2a = 34
a = 77
Now plug 77 into the other equation.
77 + b = 188
b = 111
Check your work.
77 + 111 = 188
111 - 77 = 34
I figured out the equations but I used a and b and that's as far as I got, the way you figured it out was excellent
I just subtracted 34 from 188, divided 154 by 2, got 77 and added the 34 back to one of the numbers.
111 and 77 and yes I used algebra. Specifically, started by describing the two true equations resulting from the description, then substituting and resolving for X and Y. Specifically, X+Y=188 and X=Y+34. Then the first equation can be represented as Y+34+Y=188. Then solve for Y. Once you have solved for Y you can immediately solve for X.
the sum of means a factor two. or as I do half the 188 and set a plus/ min. Like half both numbers 188/2 + or - 34/2 leads to 94 + 17 and 94 -17
I divided 188 by 2 = 94
The divided 34 by 2=17
Then added 94+17=111
And finally subtracted 94-17 =77
Actually, since I did it in my head, I think I mentally subtracted 111 from 188 to get 77 ( it was an easier subtraction)
I got the right answer. I subtracted 34 from 188 then I took 1/2 of that answer to get 77, added 34 to get 111. Your way was so much easier though .
The two numbers are 77 and 111. I came up with this answer by subtracting 34 from 188 which gave me 150 for I divided the 154 by 2 to get to equal amounts which were 77 and then I added the 34 back to the 77 to get the 111 that's how I solved it
Yes, a simple and very logical way to do it in one's head ...it takes about twelve seconds or less.
That is what I did right off the get go . Takes seconds to figure it out .
I did it this way also. Solved mentally in just a few seconds and didn't need a calculator OR algebra.
I did it similar, I halved 188 and 34 and got 94 and 17, then I added and subtracted 17 from 94.
@@eddyrourke5514That's exactly the method I used in my head in well less than a minute.
Deduct 34 from 188 = 154 /2 = 77 + 34 =111 + 77= 188 less than 3 seconds to resolve, no algebra required for a problem as basic as this. But thank you for your videos.
Total / 2 +/- delta / 2. You can use X+Y = 188 and x -y = 34. Do the substitution and solve. But that’s the hard way. Maths uses a lot of shortcuts. Remember the old sum of 1 to 100 numbers…. You can do it the hard way. Or the easy way. Short cuts will save you lots of time when testing, when you have time limits
Enjoyed this one. I did same as charlesstraight below. Your algebra solution made more logical sense though. Tip: if you want to grow your channel more you should interact with the comments, even if you just give the comments a like
New to your channel. I would like to begin with some basic skills first. Example- pre- algebra. What are some videos you could suggest to build on to the more advanced lessons.
Solution:
x + y = 188
x - y = 34
Add the two equations together to get:
x + y + x - y = 188 + 34
2x = 222 |:2
x = 111
x + y = 188
111 + y = 188 |-111
y = 77
The two numbers are 111 and 77.
Systems Of Equations
Divide both values by 2. 188/2 = 94, 34/2=17. Then subtract 17 from 94 for 77 and add 17 to 94 for 111. This was my mental process.
Dang! You had me puffing out my chest at around the 3:24 mark ... and then hit me with "... but all jokes aside..."
Setting up a system of equations of x+y=188 and under that x-y=34 adding the equations together we are left with 2x=222 dividing by 2 gets x=111 plugging 111 into the top equation 111+y=188 subtracting 111 from both sides gets y=77 putting both into second equation 111-77=34 correct thus x=111 y =77
Excellent lesson. I'm many decades removed from algebra classes and have totally forgotten how to work with linear systems.
I only took math to Grade 12. I have forgotten most of it. This is a good review but is a bit Greek to me.
I added the sum and difference. Then I divided by 2 (just as shown) to get the first number. Afterwards, I subtracted the difference from the sum and divided this by two, and got the second number.
Of course, the shown solution is a mathematically correct one and everybody should master it. But mine is faster (with such easy problems).
Haven’t done equations like these since 1970’s. Forgot how much fun they were.
Been 57 years since I took an algebra class so I forgot you could add equations. so I did it a different way....draw a line and put zero on the left end and 188 at the other end. Just from logic I can give you 2 numbers that add to 188. Its the one in the middle 188 divided by 2 is 94 , so 94 plus 94=188. to get the right answers split the difference.....34 divided by 2 is 17 so go to 94 and go 17 paces up the road and 17 paces down the road and you have your answers! Yay me.
111 + 77 = 188; 111-77 = 34
X + Y = 188; X - Y = 34
x = 188 - Y
x = 34 + Y
188 - Y = 34 + Y
188 = 34 + Y +Y
188 = 34 + 2Y
188 - 34 = 2Y
154 = 2Y
154/2 =Y
77 = Y
I subtracted 34 from 188 and divided the 154 (188-34) by 2, giveng me 77. By adding 77 and 34, I get the higher number 111 while using the lower number 77.
Got the right answer, but didn’t know the “Algebra” that was shown in the solution. I like the here’s the solution, now how to solve it format. 😊
I started by saying x+x+34=188 then taking 34 from each side and tidying up gives 2x=154. Halving each side give one of the numbers as 77. As the sum of both numbers is higher than 77 the other number must be a positive number so I just added 34 to it to get the other number of 111 ------ 2 seconds in my head. well, maybe 3 or 4
Divide 188 and 34 by 2 to get 94 and 17
Subtract 17 from 94 to get 77,add 17 to get 111
I use this method for spread and over/under
Thank goodness. I saw the previous answers and worried I was wrong. I got 111 and 77.
Same here. 😅
I've gotten into the habit of trying to solve the problem from the thumbnail, then opening the video and using the scrubber to skip to the solution. If I'm right, I don't watch the video unless I I think it might show me a better way of solving the problem; if I'm wrong, however, then I watch pretty much the whole video.
So this is where Systems of equations come in handy
(difference + sum) / 2 = the higher of the two numbers
34 + 188 = 222 (difference + sum)
222 / 2 = 111 (gives the higher of the two numbers)
111 - 34 = 77 (subtract the difference to get the lower of the two numbers)
111 + 77 = 188 (test by adding both numbers)
I divided 188 by 2, added 17 to the sum of 94 and came up with 111, the larger number. Subtracted 17 from the sum of 94 and came up with 77, the smaller number. The total of which is 188.
a+b=188
a-b=34
2a=222
A=111
B=77 system of equations add the two equations to isolate a and solve then substitute a to solve for b.
I like this explanation, as well.
I did the same as @decosse is this an other system or is it incorrect deduction?
You could emulate the matrix solution, by subtracting 1/1 * equation 1 from equation 2, and show that X is eliminated from all other equations, solve for Y then back-substitute.
It is interesting that everyone ASSUMES the "difference" means X - Y = 34. But it could be that Y - X = 34. All that is stated is that, "the difference between the two numbers is 34." In either case you get the same NUMBERS, but they get assigned to the opposite variable.
I just took a + b = 188, and added a - b = 34 to it. The result is 2a = 222, therefore a = 111. Substitute 111 for a into either equation for the value of b.
188-34=154
x=154/2=77
y=77+34=111
I divided 188 by 2 = 94 and divided 34 by 2 =17. 94 + 17 = 111 and 94 - 17 = 77
Exactly how I solved it.....
X + Y = 188, & X - Y = 34. Add both equations together. Becomes 2X = 222. (X + X = 2X. Positive Y plus Negative Y cancel out to zero. 188 + 34 = 222; so 2X = 222, divide by 2 becomes X = 111.) So 111 + Y = 188. (Subtract 111 from each side & Y = 188 - 111, or Y = 77.) Answer: 111 and 77. To check if right... 111 + 77 = 188 and 111 - 77 = 34. Is solved and verified to be correct. I used old school algebra. Others below methods of solving is kind of weird to me. But hey if it works for them...
This is the method I used.
Yup. Solve two equations. Old way, but works very well. 😀@@sonyacotton4881
Let's say the two numbers are x and y
x + y = 188
x = y + 34
y + y + 34 = 188 --> 2y = 188 - 34 = 154 --> y = 77
x = y + 34 --> x = 111
The important lesson is being able to translate the problem into equations.
Let us write down a equations, what is given:
x+y=188
x-y=34
If we add both equations, we get one equation with only one vatiable:
(x+y)+(x-y)=188+34
x+y+x-y=222
2*x=222
x=111
We can insert this result inone of the original equations:
111+y=188 => y=188-111=77
or
111-y=34 => y=111--34=77
So the solutionis x=111 and y=77.
188 Sum of 2 Numbers A
34 Dif of 2 Numbers B
94 Half of 188 A/2
77 Second Number A-(B/2)
111 First Number A+(B/2)
34 111-77 A-B
188 111+77 A+B
Why not just x + (×+34) =188? When you solve for x you get the other number with x+34.
That's the substitution method he briefly mentioned at 12:35
But you've skipped steps to get there.
I long ago forgot this method of eliminating the y variable. I just did: x+(x-34)=188 >> 2x=222 >> x = 111 >> therefore y=x-34=77
Add the two equations and two unknowns Add x +y + x-y = 188 +34. 2x = 222.
Seems the most facile method for finding the numbers is to use the Gaussian method of variable elimination. The two equations would be: x + y =188 and x - y = 34
Understood😊👍💥!
I used a more literal method for this (did some algebra my style and ended up with x = 94 +-17, x = 111, x = 77
I) a + b = 188
II) a - b = 34
I + II) 2a = 222
a = 111
I) b = 188 - a
b = 77
Answer:
1.) A + B=188 or A=188 - B
2.) A -B=34 or A=34 + B
3.) Therefore, 188 -B = 34 + B or 154=2B or 77=B
4.) A + 77 = 188 or 111 + 77 = 188
5.) A = 111 B = 77
6.) Check: 111 + 77 = 188, 111 -77 = 34
I solved this by dividing 188 by 2 which is 94. Then I divided 34 by 2 to get 17. Then I added and subtracted 17 from 94 to get the 2 numbers which are 77 and 111.
77 and 111, did that in my head in 5 sec: 188 / 2 = 94, 34 / 2 = 17, 94 - 17 = 77 and 94 + 17 = 111
The sum of the two numbers is 188. Therefore, draw a number line. Half of the 188 is 94. The differenceof these numbers is 34. Half of 34 is 17. Therefore, to the left of 94 is 94 -17 is 77. And, the right of 94 plus 17 is 111. Thus, 77, 111.
That’s basically how I solved it, no pencil needed lol. Yes still used a calculator.
That's how i solved, but in my head in a few seconds.
Yes that is how I solve it until he reminded me to use algebra then I used the substitution method. Not elimination like he did.😁
Exactly how I did it. But I did use a calculator.
Hi. Can you explain why you cut each number in half? I used substitution method but I would love to understand what you did. Thanks!
I did 188 divided by 2=94, then 34 divided by 2=17. 94-17=77. Then 188-77=111. 77 and 111 are the unknown numbers.
You sure made that a lot harder than it needs to be.
188/2=94
34/2=17
94-17=77
94+17=111
77+111=188
No paper, no calculator, just 10 seconds of time…if that.
I solved this differently. 188 divided by 2 = 94, 34 divided by 2 = 17, 94+17=111, 94-17=77.
Reading comments everyone is talking about how they got there without algebra. Well I did both but I used the substitution method instead of elimination method. Same answer of course.
Stuff like this I do in my head. Take 188 and cut it in half (94). Then take your 34 and cut it in half (17). Add 17 to 94 and then subtract 17 from 94. There are your two answers (111, 77).
In the beginning of the video, the answer is stated as (77,111). Shouldn't the answer be (111,77)? BTW, I really enjoy your videos. You are an excellent teacher!!
The answers are 116 and 72. X+Y=188 and X-Y=34; Y+Y+34=188
The whole purpose of the exercise is to perceive a system of equations and set up the problem accordingly. Since I've been doing these on Khan Academy, it was natural to see the system.
Add the two numbers and divide by 2. That's 111. Now you need 77 to get to 188. This is a shortcut, but it's not, it's just adding the equations together. Same if you subtracted the equations. It's 188-34 divided by 2 = 77.
I use this in gambling football and basketball.
Lesson#1-Take the over/under minus the spread. Divide by 2 is your loser's score. Add it back and that's your winner's score. Predicted scores of course.
Lesson #2-Don't gamble. LOL
Lesson #3-ef Algebra!
The way I used was x+y=188&2x=188-34=154so 2x=154, gives x=77&other value must be 77+34=111
Too much explanation, but thanks for the constant flow of problems nonetheless 😁
Remember he is pitching these lessons to people who maybe NEED more explanation than you.
I got it right by in my head in a few seconds - (total - the difference) (difference / 2) (that answer + diff) (188-34=154) ( 154 / 2= 77) (77+34= 111) I would always lose points by not showing my work in class. LOL
x + y = 188
x - y = 34
------------------
2x + 0 = 222
2x / 2 = 222 / 2
-------------------------
x = 111
111 + y = 188
y = 188 - 111
-------------------------
y = 77
x - y = 34
111 - 77 = 34
34 = 34
=================
x = 111, y = 77
Math is so beautiful
Doesn't seem to be the easy way. Addition is generally easier than subtraction.
x = lower number, not higher; x + 34 = y
x + x + 34 = 188
2x = 154
x = 77
y = 111 ( from 188 - 77)
I just halved the sum (94) then halved the difference (17) added 17 to 94 and subtracted 17 from 94.
111 and 77 ,simultaneous eq
subtract 34 from 188 and divide by 2. add 34 to 1 of the numbers. result, 111 and 77.
Ah heck, no idea. Ill just throw some numbers out there: How about 111 and 77. Just pulled those out of my (hfmmm) I have no idea if that's even right, but I'm gonna go with that.
a+b = 188. a-b = 34. Add the two equations: 2a = 222. a = 111. b +111 = 188 so b = 77. You don't need 18 minutes to describe this.
I used the simultaneous equation to solve.
X = 1st # Y = 2nd #
X + Y = 188
X - Y = 34
2X = 222
X = 111
Y = 188 - 111 = 77
111 + 77 = 188
111 - 77 = 34
Very basic math calculation using division, subtraction and addition.
I divided 188 in half. 34 in half. I substrates 17 from 94 and added 17 to 94.
Did this in my head and much quicker than the equation. Half is 94 take 17 off and whoop whoop. Can work out the numbers from that 77/111
X+y= 188 first eq. And x-y = 34
2x= 222 . .x= 111 y = 77
Got it.
Sum of 2 numbers = 188 and the difference is 34. What are the 2 numbers?
x + x + 34 = 188
2x + 34//2 = 188/2
x + 17 = 94
x + 17 - 17 = 94 - 17
x = 77 .. 1st #
2nd # or y = x + 34
y = x + 34
y = 77 + 34
y = 111
*didn’t want to use fractions😊
They were called simultaneous linear equations when I was at school, and this was a rambling, long-winded way to reach a simple solution.
THe sum = 188, the difference = 34. 188-34 = 154. 154/2 = 77. 77+34 = 111. So the two numbers are 77 and 111.
{94a-60b}= 34
I tested a bunch of numbers indeed! Not the right method for sure. :(
I don't deserve stars for this one. ;)
But I learned the proper method.
The problem literally spells out the two equations!
system of eq 111 and 77
THE 2 numbers are 111 and77 but I didn't probably do it the way you are going to do it