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The Salem Playhouse wants to make at least $\$6,800$ on ticket sales this year. Currently, adults' tickets cost $\$67$ and children's tickets cost $\$16$ . $\newline$ 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) 67 + x + 16 + y > 6,800 $\newline$ (B) 67x + 16y > 6,800 $\newline$ (C) $67 + x + 16 + y \geq 6,800$ $\newline$ (D) $67x + 16y \geq 6,800$

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Write two-variable inequalities: word problems

Full solution

Q. The Salem Playhouse wants to make at least

\$6,800

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

\$67

and children's tickets cost

\$16

.

\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)

67 + x + 16 + y > 6,800

\newline

(B)

67x + 16y > 6,800

\newline

(C)

67 + x + 16 + y \geq 6,800

\newline

(D)

67x + 16y \geq 6,800

Define Variables: Define the variables in terms of the given situation. The number of adults' tickets sold is represented by $x$ , and the number of children's tickets sold is represented by $y$ . The cost of an adult ticket is $\$67$ , and the cost of a children's ticket is $\$16$ .
Total Adult Revenue: Write an expression for the total revenue from adult tickets. This is done by multiplying the number of adult tickets sold $x$ by the cost per adult ticket ( $\$67$ ), which gives us $67x$ .
Total Children Revenue: Write an expression for the total revenue from children's tickets. This is done by multiplying the number of children's tickets sold $y$ by the cost per children's ticket ( $\$16$ ), which gives us $16y$ .
Combine Revenue Expressions: Combine the expressions from Step $2$ and Step $3$ to form an expression for the total revenue from both adult and children's tickets. This gives us $67x + 16y$ .
Set Revenue Inequality: Since the Salem Playhouse wants to make at least $\$6,800$ , we need to set the expression for total revenue greater than or equal to $\$6,800$ . This gives us the inequality $67x + 16y \geq 6,800$ .

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