The theater department charged $\$5$ per ticket for admission to the fall play, My Fair Lady. Additionally, they asked for a donation of $x$ dollars per ticket to help buy new costumes. On Friday night, they sold $80$ tickets to the fall play, and everyone who bought a ticket donated. $\newline$ Pick all the expressions that represent how much the theater department made on Friday. $\newline$ Multi-select Choices: $\newline$ (A) $5(80 + x)$ $\newline$ (B) $85x$ $\newline$ (C) $400 + 80x$ $\newline$ (D) $80(5 + x)$

Full solution

Q. The theater department charged

\$5

per ticket for admission to the fall play, My Fair Lady. Additionally, they asked for a donation of

x

dollars per ticket to help buy new costumes. On Friday night, they sold

80

tickets to the fall play, and everyone who bought a ticket donated.

\newline

Pick all the expressions that represent how much the theater department made on Friday.

\newline

Multi-select Choices:

\newline

(A)

5(80 + x)

\newline

(B)

85x

\newline

(C)

400 + 80x

\newline

(D)

80(5 + x)

Question Prompt: Question Prompt: Determine the expressions that correctly represent the total earnings of the theater department from ticket sales and donations on Friday night.
Calculate Ticket Revenue: Calculate the total revenue from ticket sales alone. $\newline$ Ticket price = $\$5$ , Number of tickets sold = $80$ . $\newline$ Total from ticket sales = $5 \times 80 = \$400$ .
Calculate Total Amount per Ticket: Add the donation amount to the ticket price to find the total amount paid per ticket. $\newline$ Total amount per ticket = Ticket price + Donation per ticket = $5 + x$ dollars.
Calculate Total Revenue: Calculate the total revenue including donations. $\newline$ Total revenue = Number of tickets sold $\times$ Total amount per ticket = $80 \times (5 + x)$ .
Compare Expressions: Compare the expressions given in the choices to the calculations. $\newline$ (A) $5(80 + x) = 400 + 5x$ (Incorrect, as it does not account for $x$ being multiplied by $80$ ) $\newline$ (B) $85x$ (Incorrect, does not represent total revenue, only considers donations incorrectly) $\newline$ (C) $400 + 80x$ (Correct, represents $\$400$ from ticket sales and $\$80x$ from donations) $\newline$ (D) $80(5 + x) = 400 + 80x$ (Correct, directly matches the calculation from Step $3$ )