Section 2.7 Mixture Applications and Uniform Motion 157 Answer 1. There were 80 seats in the orchestra section, and there were 40 in the balcony. Notice that the number of tickets sold times the price per ticket gives the revenue. • x adult tickets at $8 each gives a revenue of: x($8) or simply 8x. • 300 x children’s tickets at $6 each gives: (300 x)($6) or 6(300 x) This will help us set up an equation in Example 1. Solving a Mixture Problem Involving Ticket Sales Example 1 At an IMAX theater, 300 tickets were sold. Adult tickets cost $8 and tickets for children cost $6. If the total revenue from ticket sales was $2040, determine the number of each type of ticket sold. Solution: Let x represent the number of adult tickets sold. Step 1: Read the problem. 300 x is the number of children’s tickets. Step 2: Label the variables. Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve the equation. Step 6: Interpret the results. Number of tickets x 300 x 300 Revenue 8x 6(300 x) 2040 aRevenue from adult tickets $8 Tickets $6 Tickets Total b a revenue from children,s tickets b a total b revenue 8x 61300 x2 2040 8x 61300 x2 2040 8x 1800 6x 2040 2x 1800 2040 2x 240 x 120 There were 120 adult tickets sold. The number of children’s tickets is 300 x which is 180. Skill Practice 1. At a Performing Arts Center, seats in the orchestra section cost $18 and seats in the balcony cost $12. If there were 120 seats sold for one performance, for a total revenue of $1920, how many of each type of seat were sold? Avoiding Mistakes Check that the answer is reasonable. 120 adult tickets and 180 children’s tickets makes 300 total tickets. Furthermore, 120 adult tickets at $8 each amounts to $960, and 180 children’s tickets at $6 amounts to $1080. The total revenue is $2040 as expected.
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