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The orchestra in Springdale is putting on a benefit concert for the local children's hospital. Orchestra seating costs $\$43$ per ticket and balcony seating is $\$95$ . The goal is to raise at least $\$6,100$ for the hospital. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of orchestra seats sold $\newline$ $y =$ the number of balcony seats sold $\newline$ $\newline$ Choices: $\newline$ (A) $95x + 43y \geq 6,100$ $\newline$ (B) $95x + 43y \leq 6,100$ $\newline$ (C) $43x + 95y \leq 6,100$ $\newline$ (D) $43x + 95y \geq 6,100$

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Write two-variable inequalities: word problems

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Q. The orchestra in Springdale is putting on a benefit concert for the local children's hospital. Orchestra seating costs

\$43

per ticket and balcony seating is

\$95

. The goal is to raise at least

\$6,100

for the hospital.

\newline

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

\newline

x =

the number of orchestra seats sold

\newline

y =

the number of balcony seats sold

\newline

\newline

Choices:

\newline

(A)

95x + 43y \geq 6,100

\newline

(B)

95x + 43y \leq 6,100

\newline

(C)

43x + 95y \leq 6,100

\newline

(D)

43x + 95y \geq 6,100

Calculate orchestra seat revenue: Determine the cost per ticket for each type of seat. We are given that orchestra seating costs $\$43$ per ticket, which is represented by the variable $x$ . Therefore, the total revenue from orchestra seats is $43x$ .
Calculate balcony seat revenue: Determine the cost per ticket for balcony seats. We are given that balcony seating costs $\$95$ per ticket, which is represented by the variable $y$ . Therefore, the total revenue from balcony seats is $95y$ .
Combine total revenue: Combine the revenue from both types of seats to form an expression for the total revenue. The total revenue is the sum of the revenue from orchestra seats and balcony seats, which is $43x + 95y$ .
Set up inequality: Set up the inequality based on the goal of raising at least $\$6,100$ . To raise at least $\$6,100$ , the total revenue from ticket sales must be greater than or equal to $\$6,100$ . Therefore, the inequality is $43x + 95y \geq 6,100$ .

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