420 is what percent of 466 - 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 466 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 466, so we can write it down as 100%=466.
4. We know, that x% equals 420 of the output value, so we can write it down as x%=420.
5. Now we have two simple equations:
1) 100%=466
2) x%=420
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%=466/420
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 420 is what percent of 466

100%/x%=466/420
(100/x)*x=(466/420)*x       - we multiply both sides of the equation by x
100=1.1095238095238*x       - we divide both sides of the equation by (1.1095238095238) to get x
100/1.1095238095238=x
90.128755364807=x
x=90.128755364807

now we have:
420 is 90.128755364807% of 466