The sum of two whole numbers between 20 and 40 is 58.

[trollins]

I need help with a math question.

Number Sense: The sum of two whole numbers between 20 and 40 is 58. The difference of the two numbers is 12. What are the two numbers?

 

[f1player]

Let x and y be the two number you need, then:

x + y = 58 and x - y = 12

hence, x = 12 + y

Subbing into equation 1: (12 + y) + y = 58
12 + 2y = 58
2y = 46
y = 23

Therefore x = 58 - 23 = 35

 

[Denis]

Another way is put 'em one under the other:
x + y = 58
x - y = 12
Now add the equations:
2x = 70
so x = 70/2 = 35

Of course you don't always get 2 equations that permit that:
you'll learn that later...

 

[Mrspi]

I need help with a math question.

Number Sense: The sum of two whole numbers between 20 and 40 is 58. The difference of the two numbers is 12. What are the two numbers?

Since this problem is posted in the Arithmetic forum, I think that perhaps you should be able to solve it without algebra.

I'd suggest the "guess and check" method.

You know that the two numbers are between 20 and 40. You know that the sum of the two numbers is 58. Ok....

let's take a guess. Maybe one of the numbers is 21. Then what would be the other one? ......you KNOW that the sum is 58......if one is 21, then the other is 58 - 21, or 37. We also know that the difference of the two numbers is supposed to be 12. What is 37 - 21? It's 16. That's too big, so we know our original guess is wrong.

Maybe we should try something bigger than 21 for the first number. Let's try 24. Again, the sum of the two numbers is 58. If one number is 24, then the other is 58 - 24, or 34. We also know that the difference of the two numbers is supposed to be 12. What is 34 - 24? It's 10. That's too small.

Ok...when we used 21 for the first number, we got something that was too big.
When we used 24 for the first number, we got something that was too small. That tells us something important! We need to pick a number between 21 and 24....

Ok...see what you can come up with!!

 

[Denis]

Or think of it this way: lowest possible is 21, so let's go:
21 + 33 = 54 : no
22 + 34 = 56 : no
23 + 35 = 58 : bingo!

 

[nirocket]

ok so the difference is 12.
Therefore the bigger number is 12 more than the smaller number.
So 58= Big no + small no
if bigger no is 12 more than smaller no, we can make the bigger no to the smaller no by minusing 12 of the bigger no, which will cause the big no to be equal to the small no.
big no - 12 = small no
therefore we must minus 12 of 58 to get 2 small no.
58-12= 2 small no
58-12=46
46= 2 small no
1 small no= 46 divided by 2
small no= 23
now that we got the small no we can find the big no by adding 12 to the small no
big no=small no +12
big no= 23 + 12
big no = 35
now to check..............
big no + small no should equal to 58
23 + 35 =58
the condition is met
now for the second condition
big no - small no should be 12
35-23=12
the second condition is met
therefore the two numbers are
35 and 23