42.5 is what percent of 40 - 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 40 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 40, so we can write it down as 100%=40.
4. We know, that x% equals 42.5 of the output value, so we can write it down as x%=42.5.
5. Now we have two simple equations:
1) 100%=40
2) x%=42.5
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%=40/42.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 42.5 is what percent of 40

100%/x%=40/42.5
(100/x)*x=(40/42.5)*x       - we multiply both sides of the equation by x
100=0.94117647058824*x       - we divide both sides of the equation by (0.94117647058824) to get x
100/0.94117647058824=x
106.25=x
x=106.25

now we have:
42.5 is 106.25% of 40