martha received a 4% raise. Her new weekly salary is 249.60. What was her salary before the raise?

Question

I have a terrible professor. She told us the answer but not how she got it.

Answer 1

In this problem it looks like Martha received a salary we don't know prior to the 4% raise. So let's label that x.

So, if we look at an example of a similar problem of a salary that we do know then we could conjure up something like this:

Salary before raise is $100

the percent raise increase is 3%

Salary after the raise is $103.

A number sentence that we can make with this information is:

100 + 100(.03) = 103

100 + 3.00 = 103

Now let's replace the known numbers with variables that represent unknown numbers.

R = the original amount of something.

P= percent (written in decimal form)

N= New amount, current amount, sales price, Total, or other words that mean the new amount after the increase or decrease of the original amount.

For Martha's problem we are looking for the amount of money she got paid prior to the raise.

R + .04R = 249.60, Solve for R

R + .04R = 1.03R

1.04R = 249.60 Divide both sides by 1.04

R = 240. Now check your answer: 240 + 240(.04) = 249.60

The formula for determining percentage problems of this type is worth saving and understanding. The formula is:

R +/- RP = N

R=Original amount

+ or - = depends on the type of problem, i.e., increase or decrease of original amount.

P=percentage is decimal form

N= New amount

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Thank you.

Tony Julian