105.85 is what percent of 120 - 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 120 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 120, so we can write it down as 100%=120.
4. We know, that x% equals 105.85 of the output value, so we can write it down as x%=105.85.
5. Now we have two simple equations:
1) 100%=120
2) x%=105.85
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%=120/105.85
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 105.85 is what percent of 120

100%/x%=120/105.85
(100/x)*x=(120/105.85)*x       - we multiply both sides of the equation by x
100=1.1336797354747*x       - we divide both sides of the equation by (1.1336797354747) to get x
100/1.1336797354747=x
88.208333333333=x
x=88.208333333333

now we have:
105.85 is 88.208333333333% of 120