11 is what percent of 111 - 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 111 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 111, so we can write it down as 100%=111.
4. We know, that x% equals 11 of the output value, so we can write it down as x%=11.
5. Now we have two simple equations:
1) 100%=111
2) x%=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%=111/11
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 11 is what percent of 111

100%/x%=111/11
(100/x)*x=(111/11)*x       - we multiply both sides of the equation by x
100=10.090909090909*x       - we divide both sides of the equation by (10.090909090909) to get x
100/10.090909090909=x
9.9099099099099=x
x=9.9099099099099

now we have:
11 is 9.9099099099099% of 111