42.2 is what percent of 113 - 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 113 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 113, so we can write it down as 100%=113.
4. We know, that x% equals 42.2 of the output value, so we can write it down as x%=42.2.
5. Now we have two simple equations:
1) 100%=113
2) x%=42.2
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%=113/42.2
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 42.2 is what percent of 113

100%/x%=113/42.2
(100/x)*x=(113/42.2)*x       - we multiply both sides of the equation by x
100=2.6777251184834*x       - we divide both sides of the equation by (2.6777251184834) to get x
100/2.6777251184834=x
37.345132743363=x
x=37.345132743363

now we have:
42.2 is 37.345132743363% of 113