105.52 is what percent of 106 - 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 106 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 106, so we can write it down as 100%=106.
4. We know, that x% equals 105.52 of the output value, so we can write it down as x%=105.52.
5. Now we have two simple equations:
1) 100%=106
2) x%=105.52
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%=106/105.52
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 105.52 is what percent of 106

100%/x%=106/105.52
(100/x)*x=(106/105.52)*x       - we multiply both sides of the equation by x
100=1.0045489006823*x       - we divide both sides of the equation by (1.0045489006823) to get x
100/1.0045489006823=x
99.547169811321=x
x=99.547169811321

now we have:
105.52 is 99.547169811321% of 106