90 is what percent of 91 - 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 91 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 91, so we can write it down as 100%=91.
4. We know, that x% equals 90 of the output value, so we can write it down as x%=90.
5. Now we have two simple equations:
1) 100%=91
2) x%=90
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%=91/90
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 90 is what percent of 91

100%/x%=91/90
(100/x)*x=(91/90)*x       - we multiply both sides of the equation by x
100=1.0111111111111*x       - we divide both sides of the equation by (1.0111111111111) to get x
100/1.0111111111111=x
98.901098901099=x
x=98.901098901099

now we have:
90 is 98.901098901099% of 91