Question

1. 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. (2 points)
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. (2 points)

Explanation:

Step1: Substitute y = 9 into the inequality

We know the inequality is \(15.79x + 5.69y\leq125\). Substitute \(y = 9\) into it:
\(15.79x+5.69\times9\leq125\)

Step2: Calculate 5.69×9

\(5.69\times9 = 51.21\), so the inequality becomes:
\(15.79x + 51.21\leq125\)

Step3: Subtract 51.21 from both sides

\(15.79x\leq125 - 51.21\)
\(15.79x\leq73.79\)

Step4: Divide both sides by 15.79

\(x\leq\frac{73.79}{15.79}\approx4.67\)
Since \(x\) represents the number of full cases, we take the largest integer less than or equal to 4.67, which is 4.

Answer:

The maximum number of full cases of sports drinks that can be purchased is 4.