Find percentages, given percentage difference?

Question

I read a statistic that there is 18% more x than y in a certain group. x + y = 100% of the group

I'm trying to figure out what percentage of the set is x and what percentage is y.

I have found a lot of tutorials on reverse percentages, given the final number and percentage increase, but can't seem to apply it to this.

Thanks

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Applying the accepted answer below, I used simultaneous equation to solve

$$ 1) px + py = 100 $$ $$ 2) px = 1.18py$$

Substitue px into equation 1)

$$ 1) 1.18py + py = 100 $$ $$ 2.18py = 100 $$ $$ y = 45.87 $$ $$ x = 54.13 $$

I'm assuming that x being 18% greater than y would mean that we find 18% of y and add it to y to find x? $$ 45.87 + (45.87*.18) = 54.13 $$

Answer 1

You cannot know what percentage of the set is $x$, because if both $x$ and $y$ increase by the same relative amount, the claim

There is $18\%$ more $x$ than $y$

is still true.

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For example, take a group of one million examples.

If there are $118$ examples of $x$ and $100$ examples of $y$, then the claim

There is $18\%$ more $x$ than $y$

is true. However, if there are $118,000$ examples of $x$ and $100,000$ of $y$, then the claim is still true.

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However, if you know that each element of a set is either $x$ or $y$, then you have two equations for the percentage of $x$ and $y$ (let's call them $p_x$ and $p_y$).

1. The first equation tells you that each element is either $x$ or $y$, but not both: $$p_x + p_y = 1$$
2. The second equation tells you that there are $18\%$ more $x$ than $y$: $$p_x = 1.18p_y$$

You have two equations for two variables, so you can easily solve for $p_x, p_y$.

Answer 2

Hint: You know

$$ x = 1.18y . $$

Can you figure out $$ \frac{x}{x+y} ? $$