82 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 82 of the output value, so we can write it down as x%=82.
5. Now we have two simple equations:
1) 100%=105
2) x%=82
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%=105/82
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 82 is what percent of 105

100%/x%=105/82
(100/x)*x=(105/82)*x       - we multiply both sides of the equation by x
100=1.280487804878*x       - we divide both sides of the equation by (1.280487804878) to get x
100/1.280487804878=x
78.095238095238=x
x=78.095238095238

now we have:
82 is 78.095238095238% of 105