86.4 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 86.4 of the output value, so we can write it down as x%=86.4.
5. Now we have two simple equations:
1) 100%=105
2) x%=86.4
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%=105/86.4
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 86.4 is what percent of 105

100%/x%=105/86.4
(100/x)*x=(105/86.4)*x       - we multiply both sides of the equation by x
100=1.2152777777778*x       - we divide both sides of the equation by (1.2152777777778) to get x
100/1.2152777777778=x
82.285714285714=x
x=82.285714285714

now we have:
86.4 is 82.285714285714% of 105