Which Inequalities represent Susan's goal for earning money and the number of hours she can work in one week?

Question

Which Inequalities represent Susan's goal for earning money and the number of hours she can work in one week?
Susan is a college student with two part-time jobs. She earns $10 per hour tutoring elementary students in math. She earns $15 per hour cleaning in the library. Her goal is to earn at least $240 per week, but because of college, she does not work more than 20 hours each week.

Part A

Let e represent the number of hours Susan works in one week tutoring elementary students, and let c represent the number of hours Susan works in one week cleaning the library.

Which Inequalities represent Susan's goal for earning money and the number of hours she can work in one week?

Select all that apply.

A. c + e ≤ 20

B. 15c + 10e ≤ 20

C. 15c + 10e ≥ 20

D. c + e ≤ 240

E. 15c + 10e ≤ 240

F. 15c + 10e ≥ 240

 

 

 

Susan is a college student with two part-time jobs. She earns $10 per hour tutoring elementary students in math. She earns $15 per hour cleaning in the library. Her goal is to earn at least $240 per week, but because of college, she does not work more than 20 hours each week.

Part B

Which combinations allow Susan to work no more than 20 hours in one week and earn at least $240?

Select the three correct combinations

A. 9 hours tutoring and 10 hours cleaning the library

B. 10 hours tutoring and 10 hours cleaning the library

C. 11 hours tutoring and 8 hours cleaning the library

D. 12 hours tutoring and 8 hours cleaning the library

E. 13 hours tutoring and 7 hours cleaning the library

F. 14 hours tutoring and 7 hours cleaning the library

 

 

 

Answer 1

A. e + c ≤ 20       e ≤ 20 - c

F. 15c + 10e ≥ 240

 

15c + 10(20 - c) ≥ 240

15c + 200 - 10c ≥ 240

5c ≥ 40

c ≥ 8

 

e ≤ 20 - 8

e≤ 12

 

There are only two correct answers: A and D

Answer F satisfies the ≥ $240 but not the ≤ 20 hours.