156 Chapter 2 Linear Equations and Inequalities Expanding Your Skills For Exercises 69–70, find the indicated area or volume. Be sure to include the proper units and round each answer to two decimal places if necessary. 69. a. Find the area of a circle with radius 11.5 m. Use the p key on the calculator. b. Find the volume of a right circular cylinder with radius 11.5 m and height 25 m. 70. a. Find the area of a parallelogram with base 30 in. and height 12 in. b. Find the area of a triangle with base 30 in. and height 12 in. c. Compare the areas found in parts (a) and (b). h 25 m r 11.5 m r 11.5 m h 12 in. b 30 in. h 12 in. b 30 in. Section 2.7 Mixture Applications and Uniform Motion 1. Applications Involving Cost In Examples 1 and 2, we will look at different kinds of mixture problems. The first example “mixes” two types of movie tickets, adult tickets that sell for $8 and children’s tickets that sell for $6. Furthermore, there were 300 tickets sold for a total revenue of $2040. Before attempting the problem, we should try to gain some familiarity. Let’s try a few combinations to see how many of each type of ticket might have been sold. Suppose 100 adult tickets were sold and 200 children’s tickets were sold (a total of 300 tickets). • 100 adult tickets at $8 each gives 100($8) $800 • 200 children’s tickets at $6 each gives 200($6) $1200 Total revenue: $2000 (not enough) Suppose 150 adult tickets were sold and 150 children’s tickets were sold (a total of 300 tickets). • 150 adult tickets at $8 each gives 150($8) $1200 • 150 children’s tickets at $6 each gives 150($6) $900 Total revenue: $2100 (too much) As you can see, the trial-and-error process can be tedious and time-consuming. Therefore we will use algebra to determine the correct combination of each type of ticket. Suppose we let x represent the number of adult tickets, then the number of children’s tickets is the total minus x. That is, number of adult tickets, xatotal number b of tickets Number of children’s tickets 300 x. a a Number of children,b s tickets b Concepts 1. Applications Involving Cost 2. Applications Involving Mixtures 3. Applications Involving Uniform Motion
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