166.5 is what percent of 199.8 - 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 199.8 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 199.8, so we can write it down as 100%=199.8.
4. We know, that x% equals 166.5 of the output value, so we can write it down as x%=166.5.
5. Now we have two simple equations:
1) 100%=199.8
2) x%=166.5
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%=199.8/166.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 166.5 is what percent of 199.8

100%/x%=199.8/166.5
(100/x)*x=(199.8/166.5)*x       - we multiply both sides of the equation by x
100=1.2*x       - we divide both sides of the equation by (1.2) to get x
100/1.2=x
83.333333333333=x
x=83.333333333333

now we have:
166.5 is 83.333333333333% of 199.8