326 CHAPTER 6 Algebra, Graphs, and Functions Combined Variation Often in real-life situations, one variable varies as a combination of variables. The following examples illustrate the use of combined variation. Now solve for the area of the given triangle. A kbh (15)(20) 150 1 2 = = = Thus, the area of a triangle with a base of 15 in. and a height of 20 in. is 150 in.2 7 Now try Exercise 49 Summary of Variation Equations Direct Inverse Joint y kx = y k x = y kxz = Example 8 Hot Dog Price, Combined Variation The owners of Henrietta Hots determined their weekly sales of hot dogs, S, vary directly with their advertising budget, A, and inversely with their hot dog price, P. When their advertising budget is $2400 and the price of a hot dog is $6, they sell 5600 hot dogs a week. a) Write a variation equation expressing S in terms of A and P. Include the value of the constant of proportionality. b) Determine the expected sales if the advertising budget is $3200 and the hot dog price is $7. Solution a) Since S varies directly as A and inversely as P, we begin with the equation S kA P = We now determine k using the known values. k k k 5600 (2400) 6 5600 400 14 = = = Therefore, the equation for the weekly sales of hot dogs is S A P 14 . = b) S A P S 14 14(3200) 7 6400 = = = Henrietta Hots can expect to sell 6400 hot dogs a week if the advertising budget is $3200 and the hot dog price is $7. 7 Now try Exercise 51 Learning Catalytics Keyword: Angel-SOM-6.4 (See Preface for additional details.)
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