105.75 is what percent of 122.25 - 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 122.25 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 122.25, so we can write it down as 100%=122.25.
4. We know, that x% equals 105.75 of the output value, so we can write it down as x%=105.75.
5. Now we have two simple equations:
1) 100%=122.25
2) x%=105.75
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%=122.25/105.75
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 105.75 is what percent of 122.25

100%/x%=122.25/105.75
(100/x)*x=(122.25/105.75)*x       - we multiply both sides of the equation by x
100=1.1560283687943*x       - we divide both sides of the equation by (1.1560283687943) to get x
100/1.1560283687943=x
86.503067484663=x
x=86.503067484663

now we have:
105.75 is 86.503067484663% of 122.25