Find two numbers whose difference is 15 and whose sum is 53?

Answer 1

19 and 34.

Let the two numbers be x and y; then:

x - y = 15

x + y = 53

Adding the two equations gives:

2x = 68 → x = 34

Substituting for x in the second gives:

34 + y = 53 → y = 19

Checking by substituting for x and y in the first gives:

34 - 19 = 15 as required.