Find two numbers if their difference is 16 and their ratio is 5: 7.

Let us say that the numbers are x and y. The given clues are:

1. x – y = 16         (so x is the larger number)

2. y / x = 5 / 7

rewriting eqtn 2 in terms of y:

y = (5/7) x

combining 1 and 2:

x – (5/7) x = 16

(2/7) x = 16

x = 56

y = (5/7) x = 40

So the two numbers are 56 and 40.

The two numbers if their difference is 16 and their ratio is 5:7 are -56 and -40

Given

Difference =16

Ratio=5:7

First step

a - b = 16

a= 16 + b

Second step

Ratio =5:7

a/b= 5/7

Third step is to substitute:

(16 + b)/b  = 5/7

16 + b = (5b)/7

112 + 7b = 5b

2b= -112

b=-112/2

b = -56

a - b = 16

Hence

a -  -56 = 16

a = -40

Inconclusion The two numbers if their difference is 16 and their ratio is 5:7 are -56 and -40

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