Final answer:
Anthony's tutoring and babysitting hours can be represented by a system of inequalities. By graphing these inequalities, we can find the range of possible hours for each activity. Among the given points, only (7,6) is a solution to the system.
Step-by-step explanation:
To solve this problem, we need to create a system of inequalities to represent the situation and then graph these inequalities to determine Anthony's possible work hours. Let's define t as the number of hours Anthony spends on tutoring and b as the hours he spends on babysitting.
a. The system of inequalities based on the given situation is:
- 15t + 10b ≥ 125 (Anthony wants to earn at least $125 each week.)
- t + b ≤ 14 (Anthony can work no more than 14 hours a week.)
b. To graph the system of inequalities, plot two lines based on the equations 15t + 10b = 125 and t + b = 14. Then shade the region that represents the set of solutions satisfying both inequalities.
c. To determine if the given points are solutions, substitute them into both inequalities:
- (4,5): 15(4) + 10(5) = 60 + 50 = 110, which is not greater than 125. Thus, (4,5) is not a solution.
- (7,6): 15(7) + 10(6) = 105 + 60 = 165, which is greater than 125, and 7 + 6 = 13, which is less than 14. Thus, (7,6) is a solution.
- (5,10): 15(5) + 10(10) = 75 + 100 = 175, which is greater than 125, and 5 + 10 = 15, which is not less than or equal to 14. Thus, (5,10) is not a solution.