The sum of two numbers is 57. the larger number is 17 more than the smaller number. what are the numbers?

  20, 37

Step-by-step explanation:

You can usually work these "sum and difference" problems in your head.

One of the numbers is half the sum of those given; the other is half their difference.

Here, the smaller number is (57 -17)/2 = 20; the larger is 20+17 = 37.

The two numbers are 20 and 37.

Let a and b represent the numbers, and let s and d represent their sum and difference. The two equations you can write are ...

  a + b = s

  a - b = d

Adding these two equations gives ...

  (a +b) +(a -b) = (s) +(d)

  2a = s+d

  a = (s+d)/2 . . . . . . half the sum of the given numbers

Subtracting the second equation from the first gives ...

  (a +b) -(a -b) = (s) -(d)

  2b = s-d

  b = (s-d)/2 . . . . . . half the difference of the given numbers

congruent segments

step-by-step explanation: