106.5 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 106.5 of the output value, so we can write it down as x%=106.5.
5. Now we have two simple equations:
1) 100%=110
2) x%=106.5
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%=110/106.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 106.5 is what percent of 110

100%/x%=110/106.5
(100/x)*x=(110/106.5)*x       - we multiply both sides of the equation by x
100=1.0328638497653*x       - we divide both sides of the equation by (1.0328638497653) to get x
100/1.0328638497653=x
96.818181818182=x
x=96.818181818182

now we have:
106.5 is 96.818181818182% of 110