77.5 is what percent of 78 - 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 78 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 78, so we can write it down as 100%=78.
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%=78
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%=78/77.5
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 78

100%/x%=78/77.5
(100/x)*x=(78/77.5)*x       - we multiply both sides of the equation by x
100=1.0064516129032*x       - we divide both sides of the equation by (1.0064516129032) to get x
100/1.0064516129032=x
99.358974358974=x
x=99.358974358974

now we have:
77.5 is 99.358974358974% of 78