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A hockey team in Yardley has made it to the playoffs. In order to make a profit on the game, at least $\$19,000$ must be made in sales of lower-level tickets, which cost $\$74$ , and luxury box seats, which cost $\$170$ . Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x =$ the number of lower-level tickets sold $y =$ the number of luxury box tickets sold $\newline$ Choices: $\newline$ (A) 170x + 74y > 19,000 $\newline$ (B) $74x + 170y \geq 19,000$ $\newline$ (C) $170x + 74y \geq 19,000$ $\newline$ (D) 74x + 170y > 19,000

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Write a linear inequality: word problems

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Q. A hockey team in Yardley has made it to the playoffs. In order to make a profit on the game, at least

\$19,000

must be made in sales of lower-level tickets, which cost

\$74

, and luxury box seats, which cost

\$170

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

x =

the number of lower-level tickets sold

y =

the number of luxury box tickets sold

\newline

Choices:

\newline

(A)

170x + 74y > 19,000

\newline

(B)

74x + 170y \geq 19,000

\newline

(C)

170x + 74y \geq 19,000

\newline

(D)

74x + 170y > 19,000

Calculate total sales: Calculate the total sales from lower-level tickets. $\newline$ Total sales from lower-level tickets = Price per lower-level ticket $\times$ Number of lower-level tickets sold $\newline$ = $\$74 \times x$ $\newline$ = $74x$
Calculate luxury box sales: Calculate the total sales from luxury box tickets. $\newline$ Total sales from luxury box tickets = Price per luxury box ticket $\times$ Number of luxury box tickets sold $\newline$ = $\$170 \times y$ $\newline$ = $170y$
Form inequality for total sales: Combine the total sales from both types of tickets to form an inequality. $\newline$ Total sales = Sales from lower-level tickets + Sales from luxury box tickets $\newline$ = $74x + 170y$ $\newline$ The team needs to make at least $\$19,000$ , so the inequality is: $\newline$ $74x + 170y \geq 19,000$

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