90.5 is what percent of 82.5 - step by step solution

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 82.5 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 82.5, so we can write it down as 100%=82.5.
4. We know, that x% equals 90.5 of the output value, so we can write it down as x%=90.5.
5. Now we have two simple equations:
1) 100%=82.5
2) x%=90.5
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=82.5/90.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 90.5 is what percent of 82.5

100%/x%=82.5/90.5
(100/x)*x=(82.5/90.5)*x       - we multiply both sides of the equation by x
100=0.91160220994475*x       - we divide both sides of the equation by (0.91160220994475) to get x
100/0.91160220994475=x
109.69696969697=x
x=109.69696969697

now we have:
90.5 is 109.69696969697% of 82.5