Question 363090: If we increased x and y by 10%, by what percent does (x) /(x + y) change ? Found 2 solutions by Theo, ewatrrr:Answer by Theo(13342) (Show Source):
x + .10 * x = (1 + .10)*x = 1.10 * x
y + .10 * y = (1 + .10)*y = 1.10 * y
1.10 * (x + y) = 1.10 * x + 1.10 * y
your first ratio is x / (x + y)
your second ratio is 1.10x / 1/10 * (x + y)
you have a common factor of 1.10 which cancels out and you are left with x / (x + y)
since that's what you started with, the ratio becomes the same, i.e. there is a 0% change.
here's how it works.
assume x = 100 and y = 400
x / (x + y) = 100 / 500 = 1/5 = .2
increase both x and y by 10% to get:
x = 110 and y = 440
x + y = 110 + 440 = 550
take 110 / 550 = 1/5 = .2
the ratio is the same therefore the change in the ratio is 0.
if you look at 110 / 550, you will see that 110 = 100 * 1.1 and 550 = 500 * 1.10
if you take 1.10 * 100 / 1.10 * 500 you can see that the 1.10 in the numerator and in the denominator cancel out to get 100 / 500 which is what you started with.
