Question

Anthony charges $15 an hour for tutoring and $10 an hour for babysitting. He can work no more than 14 hours a week. How many hours should Anthony spend on each job if he wants to earn at least $125 each week?

A) x+y≤14; 10x+15y≥125.
B) x+y≤14; 15x+10y≥125.
C) x+y≥14; 15x+10y≥125.
D) x+y≤125; 15x+10y≥14.

Answer 1

Anthony should choose Option B given his hourly rates and time constraints. Hours of tutoring and babysitting combined should not exceed 14 hours (x + y ≤ 14), and they should ensure he earns at least $125 each week (15x + 10y ≥ 125).

Step-by-step explanation:

The student is asking about how Anthony should divide his time between tutoring and babysitting, given an hourly rate for each activity and a maximum number of hours he can work. To solve this problem, we have to set up inequalities that represent his constraints and desires.

Let x be the number of hours Anthony spends tutoring, and y be the number of hours he spends babysitting. According to the problem, Anthony charges $15 per hour for tutoring and $10 per hour for babysitting. He can work a maximum of 14 hours a week and wants to earn at least $125 each week.

Thus, the first constraint regarding his time can be expressed as x + y ≤ 14. This inequality reflects that the combined hours spent tutoring and babysitting should not exceed 14 hours. Secondly, to ensure Anthony earns at least $125, we can represent this with the inequality 15x + 10y ≥ 125. Therefore, the correct answer is Option B: x + y ≤ 14; 15x + 10y ≥ 125.

Option B expresses the time constraint and the minimum earning requirement correctly and should therefore be the selected choice.