209 is what percent of 199 - 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 199 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 199, so we can write it down as 100%=199.
4. We know, that x% equals 209 of the output value, so we can write it down as x%=209.
5. Now we have two simple equations:
1) 100%=199
2) x%=209
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%=199/209
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 209 is what percent of 199

100%/x%=199/209
(100/x)*x=(199/209)*x       - we multiply both sides of the equation by x
100=0.95215311004785*x       - we divide both sides of the equation by (0.95215311004785) to get x
100/0.95215311004785=x
105.02512562814=x
x=105.02512562814

now we have:
209 is 105.02512562814% of 199