40.5 is what percent of 52.5 - 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 52.5 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 52.5, so we can write it down as 100%=52.5.
4. We know, that x% equals 40.5 of the output value, so we can write it down as x%=40.5.
5. Now we have two simple equations:
1) 100%=52.5
2) x%=40.5
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%=52.5/40.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 40.5 is what percent of 52.5

100%/x%=52.5/40.5
(100/x)*x=(52.5/40.5)*x       - we multiply both sides of the equation by x
100=1.2962962962963*x       - we divide both sides of the equation by (1.2962962962963) to get x
100/1.2962962962963=x
77.142857142857=x
x=77.142857142857

now we have:
40.5 is 77.142857142857% of 52.5