100.5 is what percent of 105 - 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 105 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 105, so we can write it down as 100%=105.
4. We know, that x% equals 100.5 of the output value, so we can write it down as x%=100.5.
5. Now we have two simple equations:
1) 100%=105
2) x%=100.5
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%=105/100.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 100.5 is what percent of 105

100%/x%=105/100.5
(100/x)*x=(105/100.5)*x       - we multiply both sides of the equation by x
100=1.044776119403*x       - we divide both sides of the equation by (1.044776119403) to get x
100/1.044776119403=x
95.714285714286=x
x=95.714285714286

now we have:
100.5 is 95.714285714286% of 105