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A hockey team in Rockport has made it to the playoffs. In order to make a profit on the game, at least $\$14,000$ must be made in sales of lower-level tickets, which cost $\$63$ , and luxury box seats, which cost $\$110$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of lower-level tickets sold $\newline$ $y =$ the number of luxury box tickets sold $\newline$ Choices: $\newline$ (A) $63x + 110y \geq 14,000$ $\newline$ (B) $110x + 63y > 14,000$ $\newline$ (C) $110x + 63y \geq 14,000$ $\newline$ (D) $63x + 110y > 14,000$

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Write a linear inequality: word problems

Full solution

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

\$14,000

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

\$63

, and luxury box seats, which cost

\$110

.

\newline

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

\newline

x =

the number of lower-level tickets sold

\newline

y =

the number of luxury box tickets sold

\newline

Choices:

\newline

(A)

63x + 110y \geq 14,000

\newline

(B)

110x + 63y > 14,000

\newline

(C)

110x + 63y \geq 14,000

\newline

(D)

63x + 110y > 14,000

Define Variables: Define the variables based on the given information. $\newline$ We are given: $\newline$ Cost of one lower-level ticket: $\$63$ $\newline$ Cost of one luxury box seat: $\$110$ $\newline$ Minimum sales required for profit: $\$14,000$ $\newline$ Number of lower-level tickets sold: $x$ $\newline$ Number of luxury box tickets sold: $y$ $\newline$ We need to find an inequality that represents the situation where the total sales from both types of tickets are at least $\$14,000$ .
Total Sales Lower-Level: Write the expression for the total sales from lower-level tickets. The total sales from lower-level tickets can be calculated by multiplying the number of lower-level tickets sold $x$ by the cost of each lower-level ticket ( $\$63$ ). Total sales from lower-level tickets = $63 \times x = 63x$
Total Sales Luxury Box: Write the expression for the total sales from luxury box seats. $\newline$ The total sales from luxury box seats can be calculated by multiplying the number of luxury box tickets sold $y$ by the cost of each luxury box seat ( $\$110$ ). $\newline$ Total sales from luxury box seats = $110 \times y = 110y$
Combine Expressions: Combine the expressions to form the inequality. $\newline$ To make a profit, the total sales from both lower-level tickets and luxury box seats must be at least $\$14,000$ . Therefore, we add the expressions from Step $2$ and Step $3$ and set the sum to be greater than or equal to $\$14,000$ . $\newline$ Inequality: $63x + 110y \geq 14,000$

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