Question

the baseball team has $825 in their budget to buy equipment. each box of baseballs costs $28 and each helmet costs $35. what combination of boxes of baseballs, x, and helmets, y, could the coach order? a (-10, 20) b (10.5, 9) c (11, 16) d (15, 11)

Explanation:

Step1: Set up the cost - equation

Let $x$ be the number of boxes of baseballs and $y$ be the number of helmets. The total cost equation is $C = 28x+35y$, and the budget is $825$, so we need to check which pair $(x,y)$ satisfies $28x + 35y\leq825$ and also $x\geq0,y\geq0$ (since the number of items cannot be negative).

Step2: Check option A

For $x=- 10,y = 20$, the number of boxes of baseballs $x=-10$ is negative. So, option A is not valid as the number of items cannot be negative.

Step3: Check option B

For $x = 10.5,y=9$, the number of boxes of baseballs $x = 10.5$ is not a whole - number. Since we cannot buy a fraction of a box of baseballs, option B is not valid.

Step4: Check option C

Calculate the cost for $x = 11,y = 16$. Substitute into the cost equation: $28\times11+35\times16=308 + 560=868>825$. So, option C is not valid as it exceeds the budget.

Step5: Check option D

Calculate the cost for $x = 15,y = 11$. Substitute into the cost equation: $28\times15+35\times11=420+385 = 805\leq825$. This pair satisfies the budget constraint.

Answer:

D. (15, 11)