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 greater than or equal to 20 15t + 8b = 150

B.) t + b less than or equal to 20 15t + 8b greater than or equal to 150

C.) t + b less than or equal to 20 15t + 8b less than or equal to 150

D.) None of the systems shown represent this scenario.

Answer 1

The answer is B.
He can't work more than 20 hours so t+b must be less than or equal to 20.
He has to earn $150 so it cannot be less than 150. Theoretically he could earn more, e.g doing 10 hours of each job which equals $230

Therefore t + b less than or equal to 20 15t + 8b greater than or equal to 150

Answer 2

Option B is the correct answer.

Explanation:

Earning for tutoring per hour = 15$

Earning for bag boy per hour = 8$

We have Nick is only able to work up to 20 hours per week but must earn at least $150 per week and t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy.

Nick is only able to work up to 20 hours per week

t + b ≤ 20

But must earn at least $150 per week

15 t + 8 b ≥ 150

Option B is the correct answer.