77.5 is what percent of 102 - 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 102 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 102, so we can write it down as 100%=102.
4. We know, that x% equals 77.5 of the output value, so we can write it down as x%=77.5.
5. Now we have two simple equations:
1) 100%=102
2) x%=77.5
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%=102/77.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 77.5 is what percent of 102

100%/x%=102/77.5
(100/x)*x=(102/77.5)*x       - we multiply both sides of the equation by x
100=1.3161290322581*x       - we divide both sides of the equation by (1.3161290322581) to get x
100/1.3161290322581=x
75.980392156863=x
x=75.980392156863

now we have:
77.5 is 75.980392156863% of 102