86.6 is what percent of 110 - 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 110 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 110, so we can write it down as 100%=110.
4. We know, that x% equals 86.6 of the output value, so we can write it down as x%=86.6.
5. Now we have two simple equations:
1) 100%=110
2) x%=86.6
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%=110/86.6
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 86.6 is what percent of 110

100%/x%=110/86.6
(100/x)*x=(110/86.6)*x       - we multiply both sides of the equation by x
100=1.270207852194*x       - we divide both sides of the equation by (1.270207852194) to get x
100/1.270207852194=x
78.727272727273=x
x=78.727272727273

now we have:
86.6 is 78.727272727273% of 110