55.2 is what percent of 102.12 - 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 102.12 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 102.12, so we can write it down as 100%=102.12.
4. We know, that x% equals 55.2 of the output value, so we can write it down as x%=55.2.
5. Now we have two simple equations:
1) 100%=102.12
2) x%=55.2
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%=102.12/55.2
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 55.2 is what percent of 102.12

100%/x%=102.12/55.2
(100/x)*x=(102.12/55.2)*x       - we multiply both sides of the equation by x
100=1.85*x       - we divide both sides of the equation by (1.85) to get x
100/1.85=x
54.054054054054=x
x=54.054054054054

now we have:
55.2 is 54.054054054054% of 102.12