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174 Chapter 2 Linear Equations and Inequalities 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 Step 1: Read the problem. tickets sold. 300 x is the number of children’s Step 2: Label the unknowns. tickets. Skill Practice 2. 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? Classroom Example: p. 179, Exercise 14 Answer 2. There were 80 seats in the orchestra section, and there were 40 in the balcony. $8 Tickets $6 Tickets Total Number of tickets x 300 x 300 Revenue 8x 6(300 x) 2040 Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve the equation. Step 6: Interpret the results. aRevenue from adult tickets b a revenue from children,s ticketsb a total revenueb 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. 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.


miller_introductory_algebra_3e_ch1_3
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