405 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 of the output value, so we can write it down as x%=405.
5. Now we have two simple equations:
1) 100%=420
2) x%=405
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
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 405 is what percent of 420

100%/x%=420/405
(100/x)*x=(420/405)*x       - we multiply both sides of the equation by x
100=1.037037037037*x       - we divide both sides of the equation by (1.037037037037) to get x
100/1.037037037037=x
96.428571428571=x
x=96.428571428571

now we have:
405 is 96.428571428571% of 420