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The Summerfield Playhouse wants to make at least $\$5,200$ on ticket sales this year. Currently, adults' tickets cost $\$52$ and children's tickets cost $\$25$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of adults' tickets sold $\newline$ $y =$ the number of children's tickets sold $\newline$ Choices: $\newline$ (A) $25x + 52y \leq 5,200$ $\newline$ (B) $52x + 25y \leq 5,200$ $\newline$ (C) $25x + 52y \geq 5,200$ $\newline$ (D) $52x + 25y \geq 5,200$

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Write a linear inequality: word problems

Full solution

Q. The Summerfield Playhouse wants to make at least

\$5,200

on ticket sales this year. Currently, adults' tickets cost

\$52

and children's tickets cost

\$25

.

\newline

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

\newline

x =

the number of adults' tickets sold

\newline

y =

the number of children's tickets sold

\newline

Choices:

\newline

(A)

25x + 52y \leq 5,200

\newline

(B)

52x + 25y \leq 5,200

\newline

(C)

25x + 52y \geq 5,200

\newline

(D)

52x + 25y \geq 5,200

Calculate Ticket Revenue: Determine the revenue from one adult ticket and one child ticket. $\newline$ Revenue from one adult ticket: $\$52$ $\newline$ Revenue from one child ticket: $\$25$
Define Variables for Sales: Define the variables for the number of tickets sold. $\newline$ Let $x$ be the number of adults' tickets sold. $\newline$ Let $y$ be the number of children's tickets sold.
Write Total Revenue Expression: Write the expression for the total revenue from ticket sales. $\newline$ Total revenue from adults' tickets: $52x$ $\newline$ Total revenue from children's tickets: $25y$ $\newline$ Total revenue from all tickets: $52x + 25y$
Determine Revenue Goal Inequality: Determine the inequality that represents the goal for ticket sales revenue. $\newline$ The Summerfield Playhouse wants to make at least $\$5,200$ from ticket sales. $\newline$ This means the total revenue must be greater than or equal to $\$5,200$ . $\newline$ Inequality: $52x + 25y \geq 5,200$

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