165 is what percent of 166 - 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 166 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 166, so we can write it down as 100%=166.
4. We know, that x% equals 165 of the output value, so we can write it down as x%=165.
5. Now we have two simple equations:
1) 100%=166
2) x%=165
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%=166/165
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 165 is what percent of 166

100%/x%=166/165
(100/x)*x=(166/165)*x       - we multiply both sides of the equation by x
100=1.0060606060606*x       - we divide both sides of the equation by (1.0060606060606) to get x
100/1.0060606060606=x
99.397590361446=x
x=99.397590361446

now we have:
165 is 99.397590361446% of 166