42 is what percent of 406 - 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 406 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 406, so we can write it down as 100%=406.
4. We know, that x% equals 42 of the output value, so we can write it down as x%=42.
5. Now we have two simple equations:
1) 100%=406
2) x%=42
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%=406/42
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 42 is what percent of 406

100%/x%=406/42
(100/x)*x=(406/42)*x       - we multiply both sides of the equation by x
100=9.6666666666667*x       - we divide both sides of the equation by (9.6666666666667) to get x
100/9.6666666666667=x
10.344827586207=x
x=10.344827586207

now we have:
42 is 10.344827586207% of 406