52 is what percent of 42.4 - 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 42.4 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 42.4, so we can write it down as 100%=42.4.
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%=42.4
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%=42.4/52
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 42.4

100%/x%=42.4/52
(100/x)*x=(42.4/52)*x       - we multiply both sides of the equation by x
100=0.81538461538462*x       - we divide both sides of the equation by (0.81538461538462) to get x
100/0.81538461538462=x
122.64150943396=x
x=122.64150943396

now we have:
52 is 122.64150943396% of 42.4