37.8 is what percent of 46.5 - 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 46.5 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 46.5, so we can write it down as 100%=46.5.
4. We know, that x% equals 37.8 of the output value, so we can write it down as x%=37.8.
5. Now we have two simple equations:
1) 100%=46.5
2) x%=37.8
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%=46.5/37.8
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 37.8 is what percent of 46.5

100%/x%=46.5/37.8
(100/x)*x=(46.5/37.8)*x       - we multiply both sides of the equation by x
100=1.2301587301587*x       - we divide both sides of the equation by (1.2301587301587) to get x
100/1.2301587301587=x
81.290322580645=x
x=81.290322580645

now we have:
37.8 is 81.290322580645% of 46.5