0.42 is what percent of 1.05 - 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 1.05 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 1.05, so we can write it down as 100%=1.05.
4. We know, that x% equals 0.42 of the output value, so we can write it down as x%=0.42.
5. Now we have two simple equations:
1) 100%=1.05
2) x%=0.42
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%=1.05/0.42
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 0.42 is what percent of 1.05

100%/x%=1.05/0.42
(100/x)*x=(1.05/0.42)*x       - we multiply both sides of the equation by x
100=2.5*x       - we divide both sides of the equation by (2.5) to get x
100/2.5=x
40=x
x=40

now we have:
0.42 is 40% of 1.05