I wanted to generalise/formalise the "divide by two and it'll be the numbers on each side of that" intuitive approach, 'cause it should be quicker than the algebraic method, if there's a long series of integers being added together. So... Divide the total (60 in this case) by the number of addends (two in this case). The result will be the median of the series of addends. So, for instance, if five consecutive odd numbers sum to 45: 45/5 = 9 ∴ Series = 5, 7, 9, 11, 13 The algebraic method, on the other hand, takes more steps including a series of four additions. x + x + 2 + x + 4 + x + 6 + x + 8 = 45 5x + 2 + 4 + 6 + 8 = 45 5x + 20 = 45 5x = 25 x = 5 ∴ Series = 5, 7, 9, 11, 13 I normally dislike simple "intuitive" solutions to problems which are obviously chosen to be easy entry-level introductions, because they seldom generalise. But in this case it does. And fewer steps + fewer calculations = far fewer opportunities for silly errors.
Answer: 29 and 31 ---------- Let one of the odd integers be X. The consecutive odd integer of X is X+2. The sum of the above two consecutive integers is given as 60. That means, X + X +2=60 2X +2 = 60 2X = 60-2 = 58 X = 58/2 = 29 X + 2 = 29 + 2 = 31
Well, being a multiple choice question, this is easy, but lets do this algebraically. So, two consecutive odd integers add to 60. Let’s set this up as: x + y = 60 Because x and y are two consecutive odd integers, it’s easy to state the relationship between them. I’ll say y is the bigger one: y = x + 2 Plugging this into our equation: x + (x + 2) = 60 And solve: x + x + 2 = 60 2x + 2 = 60 2x = 58 x = 29 29 is an odd integers, so we’re looking good. Now: y = x + 2 y = (29) + 2 y = 29 + 2 y = 31 29+31=60, and this is the answer. By the way, option B is hilarious. NOT consecutive, NOT odd, NOT adding to 60 … throw them out the window! Questions?
You complicated it unnecessarily. All you've got to do is halve it into two lots of 30s and subtract 1 from one 30 and add it onto the other. 60 = 30 + 30 = (30-1) + (30+1) = 29 + 31. Simple.
The answer was pretty obvious but you used algebra and taught us how to use algebra to figure it out and that's good 👍
I wanted to generalise/formalise the "divide by two and it'll be the numbers on each side of that" intuitive approach, 'cause it should be quicker than the algebraic method, if there's a long series of integers being added together. So...
Divide the total (60 in this case) by the number of addends (two in this case). The result will be the median of the series of addends. So, for instance, if five consecutive odd numbers sum to 45:
45/5 = 9
∴ Series = 5, 7, 9, 11, 13
The algebraic method, on the other hand, takes more steps including a series of four additions.
x + x + 2 + x + 4 + x + 6 + x + 8 = 45
5x + 2 + 4 + 6 + 8 = 45
5x + 20 = 45
5x = 25
x = 5
∴ Series = 5, 7, 9, 11, 13
I normally dislike simple "intuitive" solutions to problems which are obviously chosen to be easy entry-level introductions, because they seldom generalise. But in this case it does. And fewer steps + fewer calculations = far fewer opportunities for silly errors.
Good grief. I practically flunked math several times and I got this immediately. Guess Im not as dumb as I always thought, lol!
If you guess how many chickens are in the bag i’l give them both to you for free ?😂😂😂😂😂
An even number is always located between 2 odd numbers
2n -1 < 2n < 2n + 1 --> e.g. 1 - 2 - 3 , 9 - 10 - 11
60 = 2n - 1 + 2n + 1
60 = 4n
60/4 = 4n/4
15 = n
60 = 2(15) - 1 + 2(15) + 1
60 = 29 + 31
c) 29 , 31 ✅
This is not an algebra question, this is a “well, duh!” question.
Divide the given number in half, go one integer either way, there you go.
Thank you
29&31
60÷2=30
balanced about 30 are
29 and 31
a+a+2=60
2a=58
a=29
a+2=31
Definition of an odd number is 2n +1. So the equation is (2n+1)+2 + (2n+1) = 60. n = 14 and 14 x 2 +1 = 29, succeding number is 31.
Answer:
29 and 31
----------
Let one of the odd integers be X.
The consecutive odd integer of X is X+2.
The sum of the above two consecutive integers is given as 60.
That means,
X + X +2=60
2X +2 = 60
2X = 60-2 = 58
X = 58/2 = 29
X + 2 = 29 + 2 = 31
29 & 31 got it in 1 second thanks for the fun.
29, 31
29 and31
Stanford University swipe cards. Valid only for university campus food and beverage. And uniforms.
(x + 1) + (x − 1) = 60
2x + 1 − 1 = 60
2x = 60
x = 30
∴ c: 29, 31
C) 29,31
Well, being a multiple choice question, this is easy, but lets do this algebraically.
So, two consecutive odd integers add to 60. Let’s set this up as:
x + y = 60
Because x and y are two consecutive odd integers, it’s easy to state the relationship between them. I’ll say y is the bigger one:
y = x + 2
Plugging this into our equation:
x + (x + 2) = 60
And solve:
x + x + 2 = 60
2x + 2 = 60
2x = 58
x = 29
29 is an odd integers, so we’re looking good. Now:
y = x + 2
y = (29) + 2
y = 29 + 2
y = 31
29+31=60, and this is the answer.
By the way, option B is hilarious. NOT consecutive, NOT odd, NOT adding to 60 … throw them out the window!
Questions?
But how about trying 30, instead of 60. Maybe two consecutive EVEN numbers.
2, 60
29+31=60 simple, very simple
You complicated it unnecessarily. All you've got to do is halve it into two lots of 30s and subtract 1 from one 30 and add it onto the other.
60 = 30 + 30
= (30-1) + (30+1)
= 29 + 31.
Simple.
C ?
C
Odd numbers are never consecutive.
They can be. Example: 1,3,5,7,9... those are written consecutively.
He didn't say "consecutive integers". He said "consecutive ODD integers". 5, 10, 15, 20 would be consecutive multiples of 5.
You don’t even have to know Algebra here Because it is a multiple choice question
29 and 31