Question

The sum of two numbers is 100. The difference between the numbers is 6. What are the two numbers?

Answer 1

53 and 47

Explanation:

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

x and y

Their sum = 100
x + y = 100
Their difference = 6
x - y = 6

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

x + y = 100 (1)
x - y = 6 (2)

Rearrange (2):

x - y = 6

x = 6 + y (3)

Substitute (3) into (1)

x + y = 100

(6 + y) + y =100

6 + y + y = 100

2y = 94

y =47 (4)

Substitute (4) into (3)

x = 6 + 47

x = 6 + 47 = 53

Hence the two numbers are 47, and 53.