40 is what percent of 415 - 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 415 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 415, so we can write it down as 100%=415.
4. We know, that x% equals 40 of the output value, so we can write it down as x%=40.
5. Now we have two simple equations:
1) 100%=415
2) x%=40
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%=415/40
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 40 is what percent of 415

100%/x%=415/40
(100/x)*x=(415/40)*x       - we multiply both sides of the equation by x
100=10.375*x       - we divide both sides of the equation by (10.375) to get x
100/10.375=x
9.6385542168675=x
x=9.6385542168675

now we have:
40 is 9.6385542168675% of 415