Rick works two jobs to pay for college. He tutors for $20 per hour and also works as a bag boy for $7 per hour. Due to his class and study schedule, Rick is only able to work up to 25 hours per week but must earn at least $200 per week. If t represents the number of hours Rick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?
t + b less than or equal to 25
20t + 7b greater than or equal to 200
t + b greater than or equal to 25
20t + 7b = 200
t + b less than or equal to 25
20t + 7b less than or equal to 200
None of the systems shown represent this scenario.
Is it a
Yes, that is the only one where he makes 200 or more
thx!!
The correct system of inequalities that represents this scenario is:
t + b ≤ 25
20t + 7b ≥ 200
The correct representation of the scenario is:
t + b less than or equal to 25
20t + 7b greater than or equal to 200
Let's break it down:
1. The first inequality, t + b less than or equal to 25, represents the fact that Rick can only work up to 25 hours per week. This includes both tutoring (t) and bag boy work (b). If the total number of hours exceeds 25, Rick will not be able to meet his class and study schedule.
2. The second inequality, 20t + 7b greater than or equal to 200, represents the fact that Rick must earn at least $200 per week. The expression 20t represents the amount of money Rick earns from tutoring ($20 per hour), and 7b represents the amount of money he earns from working as a bag boy ($7 per hour). The total earnings should be greater than or equal to $200.
Therefore, the correct system of inequalities is:
t + b less than or equal to 25
20t + 7b greater than or equal to 200
The solution to this system of inequalities will provide the range of values for t and b that meet Rick's requirements of both working up to 25 hours per week and earning at least $200 per week.