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The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most $\$770$ to purchase bats and softballs. A case of softballs has a price of $\$38$ , and a bat has a price of $\$27$ . Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x =$ the number of cases of softballs $y =$ the number of bats $\newline$ Choices: $\newline$ (A) 38x - 27y < 770 $\newline$ (B) $38x \times 27y \leq 770$ $\newline$ (C) 38x + 27y < 770 $\newline$ (D) $38x + 27y \leq 770$

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Write two-variable inequalities: word problems

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Q. The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most

\$770

to purchase bats and softballs. A case of softballs has a price of

\$38

, and a bat has a price of

\$27

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

x =

the number of cases of softballs

y =

the number of bats

\newline

Choices:

\newline

(A)

38x - 27y < 770

\newline

(B)

38x \times 27y \leq 770

\newline

(C)

38x + 27y < 770

\newline

(D)

38x + 27y \leq 770

Identify Cost and Variables: Identify the cost per item and the corresponding variables. The cost of a case of softballs is $\$38$ , and we are using the variable $x$ to represent the number of cases of softballs. The cost of a bat is $\$27$ , and we are using the variable $y$ to represent the number of bats.
Write Total Cost Expression: Write the expression for the total cost of the softballs and bats. The total cost of the softballs is $38x$ (since each case costs $\$38$ ), and the total cost of the bats is $27y$ (since each bat costs $\$27$ ). The total cost is the sum of these two amounts, which is $38x + 27y$ .
Incorporate Budget Constraint: Incorporate the budget constraint into the inequality. The coach has a budget of at most $\$770$ , which means the total cost cannot exceed this amount. Therefore, the inequality must reflect that the total cost of softballs and bats is less than or equal to $\$770$ .
Write Inequality in Standard Form: Write the inequality in standard form using the total cost expression and the budget constraint. The inequality that represents this situation is $38x + 27y \leq 770$ .
Check Answer Choices: Check the answer choices to find the inequality that matches our derived inequality. The correct choice is (D) $38x + 27y \leq 770$ , which matches the inequality we found in Step $4$ .

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