Question

Ms. Price has received a 14% raise in salary in each of the last 2 years. If her salary this year is $96,000, What was her salary 2 years ago, rounded to the nearest penny?

Answer 1

Let x be her salary of 2 years ago.

Last year, she received a 14% raise in salary, based on her initial salary, which was x.

So the raise she received was

`x\cdot(14)/(100)`

So, if we want to calculate her salary last year, we simply add the salary she had 2 years ago to the amount she got raised, so her salary last year was

`x\cdot(1+(14)/(100))`

Note that to calculate the salary of last year, we took the salary of the previous year (x) and multiply it by (1+ 14/100).

Since this year she got another 14% raise, we simply follow our principle of multiplying by (1+14/100). We take the salary of last year and multiply it by this factor, so we end up having

`x\cdot(1+(14)/(100))\cdot(1+(14)/(100))=x\cdot(1+(14)/(100))^2`

This expression would be her actual salary, which we know is 96000. So we have the equation

`x\cdot(1+(14)/(100))^2=96000`

if we divide both sides by (1+14/100)^2, we get

`x=(96000)/((1+(14)/(100))^2)=73868.8827`

which rounded to the neares penny is 73868.88