46.6 is what percent of 52 - 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 52 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 52, so we can write it down as 100%=52.
4. We know, that x% equals 46.6 of the output value, so we can write it down as x%=46.6.
5. Now we have two simple equations:
1) 100%=52
2) x%=46.6
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%=52/46.6
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 46.6 is what percent of 52

100%/x%=52/46.6
(100/x)*x=(52/46.6)*x       - we multiply both sides of the equation by x
100=1.1158798283262*x       - we divide both sides of the equation by (1.1158798283262) to get x
100/1.1158798283262=x
89.615384615385=x
x=89.615384615385

now we have:
46.6 is 89.615384615385% of 52