106.4 is what percent of 117 - 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 117 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 117, so we can write it down as 100%=117.
4. We know, that x% equals 106.4 of the output value, so we can write it down as x%=106.4.
5. Now we have two simple equations:
1) 100%=117
2) x%=106.4
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%=117/106.4
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 106.4 is what percent of 117

100%/x%=117/106.4
(100/x)*x=(117/106.4)*x       - we multiply both sides of the equation by x
100=1.0996240601504*x       - we divide both sides of the equation by (1.0996240601504) to get x
100/1.0996240601504=x
90.940170940171=x
x=90.940170940171

now we have:
106.4 is 90.940170940171% of 117