405.5 is what percent of 420 - 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 420 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 420, so we can write it down as 100%=420.
4. We know, that x% equals 405.5 of the output value, so we can write it down as x%=405.5.
5. Now we have two simple equations:
1) 100%=420
2) x%=405.5
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%=420/405.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 405.5 is what percent of 420

100%/x%=420/405.5
(100/x)*x=(420/405.5)*x       - we multiply both sides of the equation by x
100=1.035758323058*x       - we divide both sides of the equation by (1.035758323058) to get x
100/1.035758323058=x
96.547619047619=x
x=96.547619047619

now we have:
405.5 is 96.547619047619% of 420