111.65 is what percent of 100.5 - 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 100.5 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 100.5, so we can write it down as 100%=100.5.
4. We know, that x% equals 111.65 of the output value, so we can write it down as x%=111.65.
5. Now we have two simple equations:
1) 100%=100.5
2) x%=111.65
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%=100.5/111.65
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 111.65 is what percent of 100.5

100%/x%=100.5/111.65
(100/x)*x=(100.5/111.65)*x       - we multiply both sides of the equation by x
100=0.90013434841021*x       - we divide both sides of the equation by (0.90013434841021) to get x
100/0.90013434841021=x
111.09452736318=x
x=111.09452736318

now we have:
111.65 is 111.09452736318% of 100.5