Question

1) If the ratio of two numbers is 5:2, what is the ratio of their sum to their difference?

Answer 1

QUESTION 1

Let the numbers be x and y.

It was given that the numbers are in the ratio 5:2.


This implies that,


$x : y = 5 :2$


The sum of the numbers is

$x + y = 5 + 2 = 7$





The difference is
$5 - 2 = 3$




The ratio if the sum to the difference is

$7 : 3$

QUESTION 2


Let the numbers be m and n.

This implies that,

$m + n = 91...(1)$


Also,


$m : n = 6 : 7$


We rewrite this as a fraction to get,


$\frac{m}{n} = \frac{6}{7}$


We make m the subject to get,


$m = \frac{6}{7} n...(2)$
We put equation (2) into equation (1) to get,

$\frac{6}{7} n + n = 91$


$13n = 7 \times 91$


$n = \frac{7 \times 91}{13}$


$n = 49$


$m = \frac{6}{7} \times 49 = 42$


The numbers are 42 and 49.