80.5 is what percent of 102.5 - 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 102.5 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 102.5, so we can write it down as 100%=102.5.
4. We know, that x% equals 80.5 of the output value, so we can write it down as x%=80.5.
5. Now we have two simple equations:
1) 100%=102.5
2) x%=80.5
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%=102.5/80.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 80.5 is what percent of 102.5

100%/x%=102.5/80.5
(100/x)*x=(102.5/80.5)*x       - we multiply both sides of the equation by x
100=1.2732919254658*x       - we divide both sides of the equation by (1.2732919254658) to get x
100/1.2732919254658=x
78.536585365854=x
x=78.536585365854

now we have:
80.5 is 78.536585365854% of 102.5