105.5 is what percent of 116 - 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 116 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 116, so we can write it down as 100%=116.
4. We know, that x% equals 105.5 of the output value, so we can write it down as x%=105.5.
5. Now we have two simple equations:
1) 100%=116
2) x%=105.5
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%=116/105.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 105.5 is what percent of 116

100%/x%=116/105.5
(100/x)*x=(116/105.5)*x       - we multiply both sides of the equation by x
100=1.0995260663507*x       - we divide both sides of the equation by (1.0995260663507) to get x
100/1.0995260663507=x
90.948275862069=x
x=90.948275862069

now we have:
105.5 is 90.948275862069% of 116