110.5 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 110.5 of the output value, so we can write it down as x%=110.5.
5. Now we have two simple equations:
1) 100%=111
2) x%=110.5
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%=111/110.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 110.5 is what percent of 111

100%/x%=111/110.5
(100/x)*x=(111/110.5)*x       - we multiply both sides of the equation by x
100=1.0045248868778*x       - we divide both sides of the equation by (1.0045248868778) to get x
100/1.0045248868778=x
99.54954954955=x
x=99.54954954955

now we have:
110.5 is 99.54954954955% of 111