How can I find numbers which assert 0.01x * y = 0.01y * x?

Question

Yesterday, somebody told me that 45% of 37 = 37% of 45. I did the math and that's actually true.

So from that, we know that:

$${45\over 100}\times 37 = {37\over 100}\times 45$$

I want to find more numbers which fulfill this property, with something like this:

$${x\over 100}\times y = {y\over 100}\times x$$

Without fractions:

$$0.01x\times y = 0.01y\times x$$

However, I have two unknown variables and only one equation, and I'd need two to be able to find solutions.

How can I solve this equation? I'd be able to solve it if I had a system of linear equations, but I have only one...

EDIT: I've just realized... every combination of x and y will work with this. Sorry, I didn't realize it before. I (stupidly) thought it wouldn't.

Answer 1

This is always true.

$.01x*y=(.01x)y=.01(xy)=.01(yx)=(.01y)x=.01y*x$

Answer 2

You wrote this statement $$ {x\over 100}\times y = {y\over 100}\times x $$

You can write this as $$ \frac{xy}{100} = \frac{xy}{100} $$ which is true for all $x$ and $y$