Question

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

Answer 1

Answer:

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 $\frac{x}{y} = \frac{5}{7}$ --- eqn 1

Substitute the value of x in equation 1

$\begin{array}{l}{\frac{16+y}{y}=\frac{5}{7}} \\\\ {16+y=\frac{5 y}{7}} \\\\ {112+y=5 y} \\\\ {2 y=-112} \\\\ {y=-56}\end{array}$

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.

Answer 2

Answer:

40 & 56

Step-by-step 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