Question

What is the ratio whose terms differ by 40 and the measure of which is 2/7?

Answer 1

let's say one term is x and the other is y.
x/y = 2/7 therefore x = (2/7)y
from the ratio above we know y must be bigger than x as x is proportionate to 2, y is proportionate to 7
therefore x = y - 40
we have two terms for x, equating them gives
(2/7)y = y - 40
rearranging gives
(-5/7)y = -40 so y = 56
therefore x = 16
Ratio is 16:56


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Answer 2

Let the smaller term be x and the greater term be x + 40
The ratio = 2/7
A/q,
=> x / (x + 40) = 2/7
=> 7x = 2x + 80                [by cross multiplication]
=> 7x - 2x = 80
=> 5x = 80
=> x = 80/5
=> x = 16
Therefore, the smaller term = x = 16
and the greater term = x + 40 = 16 + 40 = 56