Question

The sum and the difference of two numbers is 22 and 2 respectively. Find the numbers

Answer 1

Let one number be x, and the other number be y.

x and y

Their sum = 34

x + y = 34

Their difference = 10

x - y = 10

A little angel told me, the answer is 22 and 12!

We have a pair of simultaneous equations and will solve these using substitution.

x + y = 34 (1)
x - y = 10 (2)

Rearrange (2):

x - y = 10

x = 10 + y (3)

Substitute (3) into (1)

x + y = 34

(10 + y) + y =34

10 + y + y = 34

2y = 24

y =12 (4)

Substitute (4) into (3)

x = 10 + y

x = 10 + 12 = 22

Hence the two numbers are 12, and 22.