confusing word problem

Question

An elderly couple hires a nurse through a county organization. They pay her $20 per hour for the first 20 hours. The nurse decides to donate 10% of the salary she is paid to charity. As a bonus for her work, the couple increases her pay to $25 per hour after the first 20 hours. If the nurse wants to have $1,260 after donating to charity what is the minimum number of hours she must work that month?

 

**Also, the answer key says that the answer is 60. However, when I attempt to solve this, I'm not getting that answer

Answer 1

Hi, Courtney.

This problem sounds more confusing than it really is.

 

Let's call the number of hours the nurse needs to work (over the first 20 she works), X.

 

So, she gets $20/ hour for the first 20 hours and then she gets $25/ hour for the next x hours. 

 

(20 x $20) + (25X)  is how much she makes before donating. But, if she gives 10% to charity, then she is only bringing home 90% of that.

 

Therefore, she wants:

 

.90[(20 x $20) + $25X] = $1260

.9(400 + 25X) = 1260

360 + 22.5X = 1260

22.5X = 900

X = 40

But, X is only the additional number of hours she works after the first 20, so:

She really needs to work 60 hours.