Question

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

Answer 1

40 & 56

Explanation

Use a multiple table to keep ratio.

Find correct difference by subtracting products.

___[4]__[6]__[8]__

5 [20] [30] [40]

7 [28] [42] [56]

[8] [12] [16]

5 * 8 = 40

7 * 8 = 56

56 - 40 = 16

Answer 2

The two numbers are (-40,-56) where their difference is 16 and their ratio is 5:7

Solution:

Let the two numbers be "x" and "y"

Given that the difference of two numbers is 16. So we get,

x - y = 16

On rearranging the terms we get

x = 16 + y

Their ratio is 5:7 which means
`(x)/(y) = (5)/(7)` --- eqn 1

Substitute the value of x in equation 1

`\begin{array}{l}{(16+y)/(y)=(5)/(7)} \\\\ {16+y=(5 y)/(7)} \\\\ {112+y=5 y} \\\\ {2 y=-112} \\\\ {y=-56}\end{array}`

Using the y value we find the x value.

x - y = 16

Substitute the value of y in above expression

So x - (-56) = 16,

x = -40

Hence the two numbers are x = -40 and y = -56.