40.5 is what percent of 45.5 - 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 45.5 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 45.5, so we can write it down as 100%=45.5.
4. We know, that x% equals 40.5 of the output value, so we can write it down as x%=40.5.
5. Now we have two simple equations:
1) 100%=45.5
2) x%=40.5
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%=45.5/40.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 40.5 is what percent of 45.5

100%/x%=45.5/40.5
(100/x)*x=(45.5/40.5)*x       - we multiply both sides of the equation by x
100=1.1234567901235*x       - we divide both sides of the equation by (1.1234567901235) to get x
100/1.1234567901235=x
89.010989010989=x
x=89.010989010989

now we have:
40.5 is 89.010989010989% of 45.5