# Thread: problem with fractions and proportions

1. ## problem with fractions and proportions

hi

i have a mixture which has 87% of x and 13 % of y , which cannot be seperated.

if i need to make a mixture with 99.5 % of x and 0.5 % of y, how much of x and y should i mix.

2. Hello arch

Welcome to Math Help Forum!
Originally Posted by arch
hi

i have a mixture which has 87% of x and 13 % of y , which cannot be seperated.

if i need to make a mixture with 99.5 % of x and 0.5 % of y, how much of x and y should i mix.

You don't give us any quantity of the original mixture, but let me assume that there's 1 litre, and show you how to do that. Then you can work out how to do it for any other volume.

In 1 litre of the mixture, 13%, or 0.13 litre, is y. We want to add a quantity of x so that this 0.13 litre is 0.5% of the new total volume. If we add $v$ litres of x, the new total volume is $(1+v)$ litres, and 0.5% of this is $\frac{0.5}{100}(1+v)$. So we have:

$\frac{0.5}{100}(1+v) = 0.13$

$\Rightarrow 0.5(1+v) = 13$

$\Rightarrow 1 + v = 26$

$\Rightarrow v = 25$

So for every litre of the original mixture, we must add 25 litres of x, in order to make the new mixture 99.5% x, 0.5% y.