105.2 is what percent of 118 - 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 118 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 118, so we can write it down as 100%=118.
4. We know, that x% equals 105.2 of the output value, so we can write it down as x%=105.2.
5. Now we have two simple equations:
1) 100%=118
2) x%=105.2
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%=118/105.2
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 105.2 is what percent of 118

100%/x%=118/105.2
(100/x)*x=(118/105.2)*x       - we multiply both sides of the equation by x
100=1.1216730038023*x       - we divide both sides of the equation by (1.1216730038023) to get x
100/1.1216730038023=x
89.152542372881=x
x=89.152542372881

now we have:
105.2 is 89.152542372881% of 118