QUESTION 1
Let the numbers be x and y.
It was given that the numbers are in the ratio 5:2.
This implies that,
[tex]x : y = 5 :2[/tex]
The sum of the numbers is
[tex]x + y = 5 + 2 = 7[/tex]
The difference is
[tex]5 - 2 = 3[/tex]
The ratio if the sum to the difference is
[tex]7 : 3[/tex]
QUESTION 2
Let the numbers be m and n.
This implies that,
[tex]m + n = 91...(1)[/tex]
Also,
[tex]m : n = 6 : 7[/tex]
We rewrite this as a fraction to get,
[tex] \frac{m}{n} = \frac{6}{7} [/tex]
We make m the subject to get,
[tex]m = \frac{6}{7} n...(2)[/tex]
We put equation (2) into equation (1) to get,
[tex] \frac{6}{7} n + n = 91[/tex]
[tex]13n = 7 \times 91[/tex]
[tex]n = \frac{7 \times 91}{13} [/tex]
[tex]n = 49[/tex]
[tex]m = \frac{6}{7} \times 49 = 42[/tex]
The numbers are 42 and 49.
