1. Chapter 4 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Applications of Linear Systems 1 1 4 4 3 3 2 2 4.44.4 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.

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Applications of Linear Systems Slide 4.4 - 3 Recall from Section 2.4 the six step method for solving applied problems. These slightly modified steps allow for two variables and two equations. Step 1: Read the problem carefully until you understand what is given and what is to be found. Step 2: Assign variables to represent the unknown values, using diagrams or tables as needed. Write down what each variable represents. Step 3: Write two equations using both variables. Step 5: State the answer to the problem. Is the answer reasonable? Step 4: Solve the system of two equations. Step 6: Check the answer in the words of the original problem.

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Slide 4.4 - 4 Solve problems about unknown numbers.

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Two top-grossing Disney movies in 2002 were Lilo and Stitch and The Santa Clause 2. Together they grossed $284.2 million. The Santa Clause 2 grossed $7.4 million less than Lilo and Stitch. How much did each movie gross? (Source: Variety.) EXAMPLE 1 Solving a Problem about Two Unknown Numbers Solution: Let x = gross of Lilo and Stitch in millions, andy = gross of The Santa Clause 2 in millions. Slide 4.4 - 5 Lilo and Stitch grossed 145.8 million dollars and The Santa Clause 2 grossed 138.4 million dollars.

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Solve problems about quantities and their costs. Slide 4.4 - 6

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley In 1997 – 1998, the average movie ticket (to the nearest U.S. dollar) cost $10 in Geneva and $8 in Paris. (Source: Parade, September 13, 1998.) If a group of 36 people from these two cities paid $298 for tickets to see The Rookie, how many people from each city were there? EXAMPLE 2 Solving a Problem about Quantities and Costs Solution: Slide 4.4 - 7 There were 5 people from Geneva, and 31 people from Paris that went to see The Rookie. Number ofPrice per TicketTotal Value Tickets(in dollars) Parisx88x Genevay1010y Total36 XXXXXXXX 298

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Solve problems about mixtures. Slide 4.4 - 8

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley How many liters of a 25% alcohol solution must be mixed with a 12% solution to get 13 L of a 15% solution? EXAMPLE 3 Solving a Mixture Problem Involving Percent Slide 4.4 - 9 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 13.151.95

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4 Objective 4 Solve problems about distance, rate (or speed), and time. Slide 4.4 - 10

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley In one hour, Abby can row 2 mi against the current or 10 mi with the current. Find the speed of the current and Abby’s speed in still water. EXAMPLE 4 Solving a Problem about Distance, Rate, and Time Solution: Letx = Abby’s speed in still water in mph, andy = the water speed of the current in mph. Slide 4.4 - 11 Abby’s speed in still water is 6 mph, and the speed of the current is 4 mph.