Section 2.7 Mixture Applications and Uniform Motion 173 Expanding Your Skills For Exercises 69 and 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. 360 in.2 180 in.2 The area of the triangle is one-half the area of the parallelogram. 415.48 m2 10,386.89 m3 Mixture Applications and Uniform Motion Section 2.7 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 of tickets a b Number of Number of children’s tickets 300 x. a number of adult tickets, xa b total number children,s ticketsb Concepts 1. Applications Involving Cost 2. Applications Involving Mixtures 3. Applications Involving Uniform Motion Writing Translating Expression Geometry Scientific Calculator Video Concept Connections 1. Suppose 120 sodas were sold at a concession stand. Let x represent the number of diet sodas sold. Write an expression for the number of nondiet sodas sold. Answer 1. 120 x
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