# maths question how to reverse a percentage calc.

Given the sum x - (x * 0.25) = y

how do I work out what x was if the only known number is y

If you multiply both sides of the equation by 4, you get x=4y.

No, you get

4x-x=4y

3x=4y

x=(4/3)y

I don’t. But perhaps reformatting the problem will make the answer more apparent: 25% is 1/4. So:

x - 0.25 * x = y

turns into

x - 1/4 * x = y

No you don’t. You get:

3x = 4y
x = (4/3)y

If the only known number is Y, you can’t do anything.
Y is what percent of what? Doesn’t go anywhere.

If you call the percentage P ( .25 in you equation from the OP) and that is the number you’re after then you have to know x.

(x-y)/x = P (y ≠ 25 percent of x)

But it is simpler to use y/x = P (What percentage of X is Y)
Instead of x - (x*25) = y Use x *.75 = y (y = 75% of x)

x – (x * 0.25) would be 0.75*x.
(You can either use your powers of algebra to combine like terms: 1x – 0.25x = 0.75x, or just think that if you subtract off 25% of whatever x is, you have 75% of it left.)

Then divide both sides by 0.75: x = y / 0.75

(which agrees with what others have said, since dividing by 0.75 = dividing by 3/4 = multiplying by 4/3)

Thanks all.
Turns out I’d guessed at the right modification before asking.

x = y * 1.333333333333

(which is the same as x= (4/3)y)
It wasn’t giving accurate figures (out by up to .1) but that’s because the thing I was using to check my figures was rounding down every time)