Question

The sum of two numbers is 78. Their difference is 32. What are these numbers?

Answer 1

`(1) : x+y=78" & "(2) : x-y=32, (x gt y).`

`(1)+(2) rArr 2x=110 rArr x=55.`

& then, by `(1), y=78-55=23.`

Answer 2

`55` and `23`

Explanation:

Given two numbers `a` and `b`, take their sum and difference:

`a+b`

`a-b`

Then take the sum and difference of these two expressions:

`(a+b)+(a-b) = 2a`

`(a+b)-(a-b) = 2b`

Notice that we get back to the two numbers we started with, but doubled.

So with `78` and `32`, form their sum and difference and halve the results to get the two original numbers:

`(78+32)/2 = 110/2 = 55`

`(78-32)/2 = 46/2 = 23`