364 CHAPTER 6 Algebra, Graphs, and Functions oil solutions available. How many ounces of each should Amanda mix to obtain the desired solution? x y x y 3, 0.05 0.30 0.20(3), + = + = 1.2 oz of 5% solution, 1.8 oz of 30% solution 59. MODELING—Sales Position Nathan, a luggage salesperson, is considering two job offers. At Harbor Sales, Nathan’s salary would be $249 per week plus a 15% commission of sales. At The Pampered Traveler, his salary would be $300 per week plus a 12% commission of sales. a) What weekly dollar volume of sales would Nathan need to make for the total income from both companies to be the same? y x y x 249 0.15 , 300 0.12 , $1700 = + = + b) If he expects to makes weekly sales of $2500, which company would give the greater salary? Harbor Sales 60. MODELING—Copy Service Jayne recently purchased a high-speed copier for her home office and wants to purchase a service contract on the copier. She is considering two sources for the service contract. Ace Office charges $18 a month plus 2 cents per copy. Copy Haven charges $24 a month plus 1.5 cents per copy. a) How many copies would Jayne need to make for the monthly costs of both plans to be the same? y x y x 0.02 18, 0.015 24, = + = + 1200 copies b) If Jayne plans to make 2000 copies a month, which plan would be the least expensive? Copy Haven 61. MODELING—Hardwood Floor Installation The cost to purchase a particular type of hardwood flooring at Flooring Experts is $2.65 per square foot. In addition, the installation cost is $468.75. The cost to purchase the same flooring at Hardwood Guys is $3.10 per square foot. In addition, the installation cost is $412.50. a) Determine the number of square feet of this flooring that Roberto must purchase for the total cost of the flooring and installation to be the same from both stores. 125 square feet = + = + y x y x 2.65 468.75 3.10 412.50 b) If Roberto needs to purchase and have installed 196 square feet of this flooring, which store would be less expensive? Flooring Experts 62. MODELING—Movie Society Membership Delbert is choosing between two membership options at the local movie society. A Director membership costs $250 per year, and it costs $3.75 each time Delbert sees a movie. A Producer membership costs $325 per year, and it costs $2.50 each time Delbert sees a movie. c m c m 3.75 250 2.50 325 = + = + a) How many movies would Delbert have to see in one year for the two options to cost the same amount? 60 movies b) If Delbert plans to see 100 movies in a year, which membership would be the least expensive? Producer $ $ $ $ 54. MODELING—Manufacturing Television Stands A manufacturer sells television stands for $125 per stand. The manufacturing costs consist of a fixed cost of $6750 and a production cost of $50 per stand. a) Write the cost and revenue equations. C x R x 50 6750, 125 = + = b) Graph both equations for up to and including 150 stands on the same axes. * c) Use the graph to estimate the number of stands the manufacturer must sell to break even. 90 stands d) Write the profit formula. P x 75 6750 = − e) Use the profit formula to determine the manufacturer’s profit or loss if 80 units are sold. Loss of $750 f) How many stands must the manufacturer sell in order to make a profit of $3750? 140 stands In Exercises 55– 62, write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. 55. MODELING—Volleyball Tournament At an NCAA volleyball tournament, tickets for 5 adults and 2 students cost $215. Tickets for 4 adults and 3 students cost $200. Determine the price for an adult ticket and the price for a student ticket. x y x y 5 2 215, 4 3 200, + = + = $35 for adult ticket, $20 for student ticket 56. MODELING—Landscaping The Garden Factory purchased 4 tons of topsoil and 3 tons of mulch for $1529. The next week the company purchased 2 tons of topsoil and 5 tons of mulch for $1405. Determine the price per ton for topsoil and the price per ton for mulch. x y x y 4 3 1529, 2 5 1405, + = + = $245 per ton for topsoil, $183 per ton for mulch. 57. MODELING—Chemical Mixture Antonio is a chemist and discovers he is out of 25% hydrochloric acid solution. He checks his supply shelf and finds he has a large supply of both 40% and 10% hydrochloric acid solutions. How many liters of the 40% solution and of the 10% solution should he mix to make 15 liters of 25% solution.? * 58. MODELING—Lavender Oil Amanda is a massage therapist and needs 3 ounces of a 20% lavender oil solution. Amanda has only 5% and 30% lavender $ $ $ *See Instructor Answer Appendix x y x y 15, 0.40 0.10 0.25(15), 7.5 liters of 40% solution, 7.5 liters of 10% solution + = + = Yaroslav Sabitov/Shutterstock
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