Tori works two jobs to pay for college. She tutors for $30 per hour and also works as a receptionist for $10 per hour. Due to her class and study schedule, Tori is only able to work up to 20 hours per week, but must earn at least $200 per week. If t represents the number of hours Tori tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario? t + r = 20 30t + 10r = 200 t + r

Question

Tori works two jobs to pay for college. She tutors for $30 per hour and also works as a receptionist for $10 per hour. Due to her class and study schedule, Tori is only able to work up to 20 hours per week, but must earn at least $200 per week. If t represents the number of hours Tori tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario? t + r => 20 30t + 10r = 200 t + r <= 20 30t + 10r <= 200 t + r <= 20 30t + 10r = 200 t + r <= 20 30t + 10r => 200

anonymous · Answer

30t+10r represents how much she makes in a week, and since this number has to be at least 200, we thus have the following as one of our equations:$$30t+10r \ge 200$$t+r represents how many hours she works in a week, and since this is at 20 hours maximum, we thus have the following as the other equation:$$t+r\le 20$$Does that make sense?