78.5 is what percent of 706.5 - 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 706.5 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 706.5, so we can write it down as 100%=706.5.
4. We know, that x% equals 78.5 of the output value, so we can write it down as x%=78.5.
5. Now we have two simple equations:
1) 100%=706.5
2) x%=78.5
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%=706.5/78.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 78.5 is what percent of 706.5

100%/x%=706.5/78.5
(100/x)*x=(706.5/78.5)*x       - we multiply both sides of the equation by x
100=9*x       - we divide both sides of the equation by (9) to get x
100/9=x
11.111111111111=x
x=11.111111111111

now we have:
78.5 is 11.111111111111% of 706.5