109.7 is what percent of 165 - 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 165 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 165, so we can write it down as 100%=165.
4. We know, that x% equals 109.7 of the output value, so we can write it down as x%=109.7.
5. Now we have two simple equations:
1) 100%=165
2) x%=109.7
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%=165/109.7
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 109.7 is what percent of 165

100%/x%=165/109.7
(100/x)*x=(165/109.7)*x       - we multiply both sides of the equation by x
100=1.5041020966272*x       - we divide both sides of the equation by (1.5041020966272) to get x
100/1.5041020966272=x
66.484848484848=x
x=66.484848484848

now we have:
109.7 is 66.484848484848% of 165