40 is what percent of 102.4 - 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 102.4 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 102.4, so we can write it down as 100%=102.4.
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%=102.4
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%=102.4/40
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 102.4

100%/x%=102.4/40
(100/x)*x=(102.4/40)*x       - we multiply both sides of the equation by x
100=2.56*x       - we divide both sides of the equation by (2.56) to get x
100/2.56=x
39.0625=x
x=39.0625

now we have:
40 is 39.0625% of 102.4