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The Oakland City Ballet is selling tickets for an upcoming performance, and the ballet company hopes to bring in at least $\$5,900$ in revenue. Regular tickets cost $\$49$ , whereas discounted tickets cost $\$23$ . Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x =$ the number of regular tickets sold $y =$ the number of discounted tickets sold $\newline$ Choices: $\newline$ (A) $49x + 23y \leq 5,900$ $\newline$ (B) $49 + x + 23 + y \leq 5,900$ $\newline$ (C) $49 + x + 23 + y \geq 5,900$ $\newline$ (D) $49x + 23y \geq 5,900$

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Write a linear inequality: word problems

Full solution

Q. The Oakland City Ballet is selling tickets for an upcoming performance, and the ballet company hopes to bring in at least

\$5,900

in revenue. Regular tickets cost

\$49

, whereas discounted tickets cost

\$23

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

x =

the number of regular tickets sold

y =

the number of discounted tickets sold

\newline

Choices:

\newline

(A)

49x + 23y \leq 5,900

\newline

(B)

49 + x + 23 + y \leq 5,900

\newline

(C)

49 + x + 23 + y \geq 5,900

\newline

(D)

49x + 23y \geq 5,900

Calculate Regular Ticket Revenue: Determine the revenue from selling one regular ticket. $\newline$ Revenue from one regular ticket = $\$49$ $\newline$ Number of regular tickets sold = $x$ $\newline$ Total revenue from regular tickets = $49 \times x = 49x$
Calculate Discounted Ticket Revenue: Determine the revenue from selling one discounted ticket. $\newline$ Revenue from one discounted ticket = $\$23$ $\newline$ Number of discounted tickets sold = $y$ $\newline$ Total revenue from discounted tickets = $23 \times y = 23y$
Combine Regular and Discounted Revenue: Combine the revenues from regular and discounted tickets to form an expression for total revenue. $\newline$ Total revenue = Revenue from regular tickets + Revenue from discounted tickets $\newline$ Total revenue = $49x + 23y$
Formulate Revenue Inequality: Formulate the inequality based on the company's goal. $\newline$ The company hopes to bring in at least $\$5,900$ in revenue. $\newline$ This means the total revenue should be greater than or equal to $\$5,900$ . $\newline$ Inequality: $49x + 23y \geq 5,900$

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