John's annual salary after a raise of 15% is $45,000. What was his salary before the raise?
The answer to this is that John's previous salary was right about $39,130. Here is how you can find this answer:
Set up the equation like this:
45000/x = 115/100
This is because the relationship between 45000 and x (the original salary) is the same as the relationship between 115 and 100 (the new salary is 115% of the old).
Now you can cross multiply. We will multiply 45000 by 100 and 115 by x. That leaves us with
4,500,000 = 115x
divide both sides by 115 and you get
x = 39,130.43
Let us assume that John's salary before the raise was x
Then they gave him a 15% raise on his salary of x
Then, his current salary= original salary + The raise
45,000 = x + 0.15 x
45,000 = 1.15 x
==> x = 45,000/1.15 = 39,130 (approx.)
Most teachers want you to show steps to answer. but if all you want is the answer, then this shortcut equation will suffice-> 45000/1.15 = 39130.43
When an original amount or any other quantity is increased or raised by a given percentage the relationship between the original and the increased amount is given by the following formula.
x' = x*(100+p)/100 ... (1)
x = x'*100/(100+p) ... (2)
x = original amount
x' = increased amount
p = percentage increase
In the question it is given that:
Salary after raise = x' = $45000
Percentage raise = p = 15
We have to find salary before raise, that is x.
Substituting values of x' and p in the formula (2) we get:
x = 45000*100/(100 + 15) = 4500000/115 = 39130.43
John's salary before raise was $39130.43
Let us assume that John's salary before the raise was y.
John's salary was increased by 15%
So John's salary after the increase will be: 15/100 x y = 15y/100
Therefore, y + 15y/100 = 45,000
100y + 15y = 45,000
115y = 4,500,000
Answer: John's annual salary before the raise was $ 39,130.43
If we assume Jhons sary at 100, after a ruse of 15% his salary is 100+15%0f 100 = 115.
So for a afetr rise of 15%, the present salary of %45000 and the 115 should a same ratio to his salary before rise to $100
salary before /100 = present salary/115 = 45000/115.
Salary before rise = (45000/115)100 = $39,130.43