# The sum of two numbers is 37. The smaller is 17 less than the larger number. What are the numbers?

### 2 Answers | Add Yours

Let the numbers be x and y such that y > x.

Given that the sum of the numbers is 37.

==> x + y= 37 ..............(1)

Also, we are given that the smallerĀ (x) is 17 less that the larger (y).

==> y= x-17 .................(2)

Now we will substitute with (2) into (2).

==> x + y= 37

==> x+ (x-17)= 37

==> 2x -17 = 37

==> 2x = 54

==> x = 54/2 = 27

==> y= 27-17 = 10

**Then, the numbers are 27 and 10.**

For this problem use the equation

x - 17 + x = 37 with " x " representing the larger numberĀ

Now combine the like terms ( the like terms are " x " with " x " ) By combining the like terms, you should get

2x - 17 = 37 now add 17 on both sides

By adding, you should get

2x = 54 now divide by 2 on both sides

By dividing, you should get

x = 27 which is your answer for the larger number

Now use this equation to solve the answer for the smaller number

27 - 17 = smaller number

So your answer is larger number is 27 and the smaller number is 10