82.5 is what percent of 205 - 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 205 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 205, so we can write it down as 100%=205.
4. We know, that x% equals 82.5 of the output value, so we can write it down as x%=82.5.
5. Now we have two simple equations:
1) 100%=205
2) x%=82.5
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%=205/82.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 82.5 is what percent of 205

100%/x%=205/82.5
(100/x)*x=(205/82.5)*x       - we multiply both sides of the equation by x
100=2.4848484848485*x       - we divide both sides of the equation by (2.4848484848485) to get x
100/2.4848484848485=x
40.243902439024=x
x=40.243902439024

now we have:
82.5 is 40.243902439024% of 205