31.11 is what percent of 40 - 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 40 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 40, so we can write it down as 100%=40.
4. We know, that x% equals 31.11 of the output value, so we can write it down as x%=31.11.
5. Now we have two simple equations:
1) 100%=40
2) x%=31.11
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%=40/31.11
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 31.11 is what percent of 40

100%/x%=40/31.11
(100/x)*x=(40/31.11)*x       - we multiply both sides of the equation by x
100=1.2857602057216*x       - we divide both sides of the equation by (1.2857602057216) to get x
100/1.2857602057216=x
77.775=x
x=77.775

now we have:
31.11 is 77.775% of 40