82.5 is what percent of 177.5 - 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 177.5 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 177.5, so we can write it down as 100%=177.5.
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%=177.5
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%=177.5/82.5
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 177.5

100%/x%=177.5/82.5
(100/x)*x=(177.5/82.5)*x       - we multiply both sides of the equation by x
100=2.1515151515152*x       - we divide both sides of the equation by (2.1515151515152) to get x
100/2.1515151515152=x
46.478873239437=x
x=46.478873239437

now we have:
82.5 is 46.478873239437% of 177.5