Question

The senior class at Hills High School is purchasing sports drinks and bottled water to sell at the school field day. At the local discount store, a case of sports drinks costs $15.79, and a case of bottled water costs $5.69. The senior class has $125 to spend on the drinks. If x represents the number of cases of sports drinks and y represents the number of cases of bottled water purchased, write an inequality that models this situation Nine cases of bottled water are purchased for this year's field day. Use your inequality to determine algebraically the maximum number of full cases of sports drinks that can be purchased.

Answer 1

To find the maximum number of full cases of sports drinks that can be purchased, we use the inequality 15.79x + 5.69y <= 125, with y=9. After subtracting the cost of bottled water from the budget, we divide the remaining budget by the price per case of sports drinks, resulting in a purchase of 4 full cases.

Step-by-step explanation:

The situation described in the question can be modeled by the inequality 15.79x + 5.69y ≤ 125. Given that y=9 cases of bottled water are purchased, we plug this value into the inequality to solve for x, which represents the maximum number of full cases of sports drinks that can be purchased.

First, we'll calculate the total cost for the 9 cases of bottled water:

5.69 × 9 = 51.21

Then we subtract this amount from the total budget:

125 - 51.21 = 73.79

Now we can determine the maximum number of cases of sports drinks by dividing that remainder by the price per case of sports drinks:

73.79 ÷ 15.79 = approximately 4.67

Since we cannot buy a fraction of a case, the maximum number of full cases of sports drinks that can be purchased is 4 cases.