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.
Pick all the expressions that represent how much the theater department made on Friday.
5(80+x)
85x
400+80x
80(5+x)
To find out how much the theater department made on Friday, we need to account for both the price of the tickets and the donations. Let's break down the ticket price and the donation:
- They charged $5 per ticket, and they sold 80 tickets. So the revenue from ticket sales alone is 80 tickets * $5/ticket = $400.
- Each ticket also had a donation of x dollars. Since they sold 80 tickets, and everyone donated, the total amount from donations is 80 tickets * x dollars/ticket = 80x dollars.
Combining these two amounts gives us the total revenue for the theater department on Friday:
$400 (from ticket sales) + 80x (from donations) = 400 + 80x
Now let's evaluate the proposed expressions:
1. 5(80+x) - This expression represents 5 times the sum of 80 and x. This doesn't correctly represent the total revenue because it applies the $5 ticket price to both the tickets sold and the donations, which is incorrect.
2. 85x - This expression represents 85 times x, which implies a donation of $85 per ticket, not including the base ticket price. This is not the right expression.
3. 400+80x - This expression correctly represents the sum of the ticket sales ($400) and the total donation amount (80x). So, this is one correct expression for the total revenue on Friday.
4. 80(5+x) - This expression multiplies 80 by the sum of $5 and x. This also correctly accounts for the $5 ticket price and the x dollar donation for each of the 80 tickets sold. Therefore, this is another correct expression for the total revenue on Friday.
To conclude, the expressions that represent how much the theater department made on Friday are:
- 400 + 80x
- 80(5+x)