80.8 is what percent of 105.2 - 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 105.2 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 105.2, so we can write it down as 100%=105.2.
4. We know, that x% equals 80.8 of the output value, so we can write it down as x%=80.8.
5. Now we have two simple equations:
1) 100%=105.2
2) x%=80.8
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%=105.2/80.8
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 80.8 is what percent of 105.2

100%/x%=105.2/80.8
(100/x)*x=(105.2/80.8)*x       - we multiply both sides of the equation by x
100=1.3019801980198*x       - we divide both sides of the equation by (1.3019801980198) to get x
100/1.3019801980198=x
76.80608365019=x
x=76.80608365019

now we have:
80.8 is 76.80608365019% of 105.2