48 is what percent of 416 - 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 416 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 416, so we can write it down as 100%=416.
4. We know, that x% equals 48 of the output value, so we can write it down as x%=48.
5. Now we have two simple equations:
1) 100%=416
2) x%=48
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%=416/48
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 48 is what percent of 416

100%/x%=416/48
(100/x)*x=(416/48)*x       - we multiply both sides of the equation by x
100=8.6666666666667*x       - we divide both sides of the equation by (8.6666666666667) to get x
100/8.6666666666667=x
11.538461538462=x
x=11.538461538462

now we have:
48 is 11.538461538462% of 416