Question

Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week, but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?

A. t + b 20
15t + 8b = 150

B. t + b 20
15t + 8b 150

C. t + b 20
15t + 8b 150

D. None of the systems shown represent this scenario.

Answer 1

If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, we know he can only work up to 20 hrs per week, so the number of hours he tutors plus the number of hours as a bag boy have to add to less than or equal to 20. How would you write that as a mathematical expression?

Answer 2

t + b (equal to or >) 20 ?

Answer 3

close\[t+b \le20\] Nick has to work 20 hours or less.

If Nick must earn at least $150 per week, he tutors for $15 per hour and works as a bag boy for $8 per hour. The total he makes can be calculated as the rate per hour of a job multiplied by the number of hours he works at that job. So how would you write that mathematical expression?

Answer 4

The total he makes can be calculated as the rate per hour of a job multiplied by the number of hours he works at that job.
\[15t +8b \ge150\]