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

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Suresh Rawal
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Nov 4, 2016

#### Answer:

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.

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