52 is what percent of 46.4 - 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 46.4 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 46.4, so we can write it down as 100%=46.4.
4. We know, that x% equals 52 of the output value, so we can write it down as x%=52.
5. Now we have two simple equations:
1) 100%=46.4
2) x%=52
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%=46.4/52
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 52 is what percent of 46.4

100%/x%=46.4/52
(100/x)*x=(46.4/52)*x       - we multiply both sides of the equation by x
100=0.89230769230769*x       - we divide both sides of the equation by (0.89230769230769) to get x
100/0.89230769230769=x
112.06896551724=x
x=112.06896551724

now we have:
52 is 112.06896551724% of 46.4