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

Chapter Chapter 44Section Section 44

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


Applications of Linear Systems

11

44

33

22

4.44.44.44.4Solve problems about unknown numbers.Solve problems about quantities and their costs.Solve problems about mixtures.Solve problems about distance, rate (or speed), and time.


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.


Objective 11

Slide 4.4 - 4

Solve problems about unknown numbers.


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 1Solving a Problem about Two Unknown Numbers

Solution:Let x = gross of Lilo and Stitch in millions,and y = gross of The Santa Clause 2 in millions.

Slide 4.4 - 5

284.2x y 7.4x y

7.4 27 84.2. 7.44 y y 2 27

2 2

6.8y

138.4y

8.7.4 13 4x 145.8x

Lilo and Stitch grossed 145.8 million dollars and The Santa Clause 2 grossed 138.4 million dollars.


Objective 22

Solve problems about quantities and their costs.

Slide 4.4 - 6


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 2Solving a Problem about Quantities and Costs

Solution:

Slide 4.4 - 7

36x y 8 10 298x y

8 10 29836 yy 22 888 88 21 9 80 2 8 8y y

2 0

2 2

1y

5y 31x

There were 5 people from Geneva, and 31 people from Paris that went to see The Rookie.

Number of Price per Ticket Total Value

Tickets (in dollars) (in dollars)

Paris x 8 8x

Geneva y 10 10y

Total 36 XXXXXXXX 298

6 53x


Objective 33

Solve problems about mixtures.

Slide 4.4 - 8


How many liters of a 25% alcohol solution must be mixed with a 12% solution to get 13 L of a 15% solution?

EXAMPLE 3Solving a Mixture Problem Involving Percent

Slide 4.4 - 9

Solution:13x y

.12 .25 1.95x y

.12 .25 1100 100.95x y 12 25 19513 yy

156 12 25 15 195 566 1y y 13 1

3

3

1 39y 3 31x

To make 13 L of a 15% solution, 3 L of 25% solution, and 10 L of 12% solution must be used.

Liters of Percent (as Liters of

Solution a decimal) pure alcohol

x .12 .12x

y .25 .25y

13 .15 1.95

3y 10x


Objective 44

Solve problems about distance, rate (or speed), and time.

Slide 4.4 - 10


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 4Solving a Problem about Distance, Rate, and Time

Solution:Let x = Abby’s speed in still water in mph,and y = the water speed of the current in mph.

Slide 4.4 - 11

10x y

2x y

22 1 20y y

Abby’s speed in still water is 6 mph, and the speed of the current is 4 mph.

2 8

2 2

y

4y

2 4x 6x

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

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