Chapter 4 Section 4
Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Applications of Linear Systems Solve problems about unknown numbers. Solve problems about quantities and their costs. Solve problems about mixtures. Solve problems about distance, rate (or speed), and time
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Applications of Linear Systems Recall from Section 2.4 the six step method for solving applied problems. These slightly modified steps allow for two variables and two equations. Solving an Applied Problem with Two Variables Step 1: Read the problem carefully. What information is given? What are you asked to find? Step 2: Assign variables to represent the unknown values. Use a sketch, diagram, or table, as needed. Write down what each variable represents. Step 3: Write two equations using both variables. Step 5: State the answer. Label it appropriately. Does it seem reasonable? Step 4: Solve the system of two equations. Step 6: Check the answer in the words of the original problem. Slide 4.4-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Solve problems about unknown numbers. Slide 4.4-4
Copyright © 2012, 2008, 2004 Pearson Education, Inc. In 2008, spending on sporting equipment and recreational transport totaled $51,879 million. Spending on recreational transport exceeded spending on sporting equipment by $2113 million. How much was spent on each? (Source: National Sporting Goods Association.) Solution: There was $24,883 million spent on sporting equipment and $26,996 spent on recreational transport. Slide EXAMPLE 1 Solving a Problem about Two Unknown Numbers Let x = sales of sporting equipment in millions of dollars. Let y = sales of recreational transport in millions of dollars.
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Solve problems about quantities and their costs. Slide 4.4-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc. There were 5 main floor tickets and 14 mezzanine tickets bought. For a production of Wicked at the Pantages Theatre in Los Angeles, main floor tickets cost $96 and mid-priced mezzanine tickets cost $58. If a group of 18 people attended the show and spent a total of $1234 for their tickets, how many of each kind of ticket did they buy? (Source: Solution: Let x = the number of main floor tickets and y = the number of mezzanine tickets. Slide EXAMPLE 2 Solving a Problem about Quantities and Costs Number ofPrice per TicketTotal Value Tickets(in dollars) Main Floorx9696x Mezzaniney5858y Total18XXXXXXXXXXX1234
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Solve problems about mixtures. Slide 4.4-8
Copyright © 2012, 2008, 2004 Pearson Education, Inc. How many liters of a 25% alcohol solution must be mixed with a 12% solution to get 13 L of a 15% solution? Solution: To make 13 L of a 15% solution, 3 L of 25% solution, and 10 L of 12% solution must be used. Liters ofPercent (asLiters of Solutiona decimal)pure alcohol x.12.12x y.25.25y Slide EXAMPLE 3 Solving a Mixture Problem Involving Percent
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 4 Solve problems about distance, rate (or speed), and time. Slide
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Two cars that were 450 mi apart traveled towards each other. They met after 5 hr. If one car traveled twice as fast as the other, what were their rates? Solution: Letx = the rate of the slower car, andy = the rate of the faster car. The faster car travels 60 mph and the slower car travels 30 mph. Slide EXAMPLE 4 Solving a Problem about Distance, Rate, and Time rtd Faster Cary55y5y Slower Carx55x5x