Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 1

Whole Numbers

1-7-2Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Section 1.7

Solving Application Problems

1-7-3Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Key Words and Phrases for Solving Application Problems

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Steps for Solving Application Problems

1-7-5Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Example

• An online retailer shipped multiple orders on one day. The orders were for $27, $54, $62, and $91. What is the total value of the orders shipped that day?

1-7-6Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the dollar amounts for various shipments. We are asked to find a total.

• Take inventory.The knowns are the amounts of the shipments.The unknown is the total amount of the shipments.

1-7-7Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the dollar amounts for various shipments. We are asked to find a total.

• Take inventory.The knowns are the amounts of the shipments.The unknown is the total amount of the shipments.

1-7-8Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the dollar amounts for various shipments. We are asked to find a total.

• Take inventory.The knowns are the amounts of the shipments.The unknown is the total amount of the shipments.

1-7-9Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the dollar amounts for various shipments. We are asked to find a total.

• Take inventory.The knowns are the amounts of the shipments.The unknown is the total amount of the shipments.

1-7-10Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The keyword total indicates that we must add the amounts of the shipments.

• Solve the problem.Add.

2

$234

7

54

62

91+

1-7-11Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The keyword total indicates that we must add the amounts of the shipments.

• Solve the problem.Add.

2

$234

7

54

62

91+

1-7-12Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The keyword total indicates that we must add the amounts of the shipments.

• Solve the problem.Add.

2

$234

7

54

62

91+

1-7-13Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The keyword total indicates that we must add the amounts of the shipments.

• Solve the problem.Add.

2

$234

7

54

62

91+

1-7-14Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The keyword total indicates that we must add the amounts of the shipments.

• Solve the problem.Add.

2

$234

7

54

62

91+

1-7-15Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Check the solution.To check, add again. Alternatively, estimate the solution by rounding the amount to the leftmost digit. Add. The estimate, $230, indicates that our solution is reasonable.

30

50

60

90

$230

+

1-7-16Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Check the solution.To check, add again. Alternatively, estimate the solution by rounding the amount to the leftmost digit. Add. The estimate, $230, indicates that our solution is reasonable.

30

50

60

90

$230

+

1-7-17Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Example

• A jeweler has a supply of multicolored gems to put in display boxes. The jeweler has a total of 104 gems and plans to use 13 display boxes. How many gems will be placed in each box if they are to be equally divided?

1-7-18Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the fact that the total number of gems must be distributed evenly among a given number of display boxes. We are asked for the number of gems to be placed in each box.

• Take inventory.The knowns are the total number of gems and the number of boxes. The unknown is the number of gems per box.

1-7-19Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the fact that the total number of gems must be distributed evenly among a given number of display boxes. We are asked for the number of gems to be placed in each box.

• Take inventory.The knowns are the total number of gems and the number of boxes. The unknown is the number of gems per box.

1-7-20Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the fact that the total number of gems must be distributed evenly among a given number of display boxes. We are asked for the number of gems to be placed in each box.

• Take inventory.The knowns are the total number of gems and the number of boxes. The unknown is the number of gems per box.

1-7-21Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.We are given the fact that the total number of gems must be distributed evenly among a given number of display boxes. We are asked for the number of gems to be placed in each box.

• Take inventory.The knowns are the total number of gems and the number of boxes. The unknown is the number of gems per box.

1-7-22Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The key phrase equally divided indicates that we must divide the total number of gems by the number of boxes.

• Solve the problem.Divide.

813 104

104

0

1-7-23Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The key phrase equally divided indicates that we must divide the total number of gems by the number of boxes.

• Solve the problem.Divide.

813 104

104

0

1-7-24Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The key phrase equally divided indicates that we must divide the total number of gems by the number of boxes.

• Solve the problem.Divide.

813 104

104

0

1-7-25Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The key phrase equally divided indicates that we must divide the total number of gems by the number of boxes.

• Solve the problem.Divide.

813 104

104

0

1-7-26Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Translate the problem.The key phrase equally divided indicates that we must divide the total number of gems by the number of boxes.

• Solve the problem.Divide.

813 104

104

0

1-7-27Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Check the solution.To check, multiply the total number of boxes by the quotient. Since this product equals the total number of gems, our solution checks.

13

8

104

´

1-7-28Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Check the solution.To check, multiply the total number of boxes by the quotient. Since this product equals the total number of gems, our solution checks.

13

8

104

´

1-7-29Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Example

• A television station has 48 minutes of paid advertisements to be broadcast during eight equal-length shows. The total length of programming is 240 minutes including commercials. How long is each show?

1-7-30Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.This problem has two parts.Part 1: Find the number of minutes of programming without commercials.Part 2: Find the length of each show.

1-7-31Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.This problem has two parts.Part 1: Find the number of minutes of programming without commercials.Part 2: Find the length of each show.

1-7-32Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution

• Understand the situation.This problem has two parts.Part 1: Find the number of minutes of programming without commercials.Part 2: Find the length of each show.

1-7-33Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Take inventory.The knowns are the total length of programming and the total number of minutes of commercials. The unknown is the total minutes of the eight shows.

• Translate the problem.Find the total minutes of the eight shows by subtracting the total minutes of commercials from the total minutes of programming.

1-7-34Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Take inventory.The knowns are the total length of programming and the total number of minutes of commercials. The unknown is the total minutes of the eight shows.

• Translate the problem.Find the total minutes of the eight shows by subtracting the total minutes of commercials from the total minutes of programming.

1-7-35Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Take inventory.The knowns are the total length of programming and the total number of minutes of commercials. The unknown is the total minutes of the eight shows.

• Translate the problem.Find the total minutes of the eight shows by subtracting the total minutes of commercials from the total minutes of programming.

1-7-36Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Take inventory.The knowns are the total length of programming and the total number of minutes of commercials. The unknown is the total minutes of the eight shows.

• Translate the problem.Find the total minutes of the eight shows by subtracting the total minutes of commercials from the total minutes of programming.

1-7-37Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Solve the problem.Subtract. 240 – 48 = 192 minutes

• Check the solution.Check by adding the total number of minutes for the eight shows to the number of minutes for commercials. 192 + 48 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

1-7-38Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Solve the problem.Subtract. 240 – 48 = 192 minutes

• Check the solution.Check by adding the total number of minutes for the eight shows to the number of minutes for commercials. 192 + 48 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

1-7-39Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Solve the problem.Subtract. 240 – 48 = 192 minutes

• Check the solution.Check by adding the total number of minutes for the eight shows to the number of minutes for commercials. 192 + 48 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

1-7-40Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 1

• Solve the problem.Subtract. 240 – 48 = 192 minutes

• Check the solution.Check by adding the total number of minutes for the eight shows to the number of minutes for commercials. 192 + 48 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

1-7-41Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Take inventory.The knowns are the total length of the eight shows, 192 minutes, and the fact that there are eight shows. The unknown is the length of each show.

• Translate the problem.Find the length of each show by dividing the total length of the shows by the number of shows.

1-7-42Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Take inventory.The knowns are the total length of the eight shows, 192 minutes, and the fact that there are eight shows. The unknown is the length of each show.

• Translate the problem.Find the length of each show by dividing the total length of the shows by the number of shows.

1-7-43Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Take inventory.The knowns are the total length of the eight shows, 192 minutes, and the fact that there are eight shows. The unknown is the length of each show.

• Translate the problem.Find the length of each show by dividing the total length of the shows by the number of shows.

1-7-44Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Take inventory.The knowns are the total length of the eight shows, 192 minutes, and the fact that there are eight shows. The unknown is the length of each show.

• Translate the problem.Find the length of each show by dividing the total length of the shows by the number of shows.

1-7-45Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Solve the problem.Divide. Each show is 24 minutes long.

• Check the solution.To check, multiply the length of each show by the number of shows. 24 × 8 = 192.Since this product equals the number of minutes of programming without commercials, the answer checks.

8 192

16

32

32

24

0

1-7-46Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Solve the problem.Divide. Each show is 24 minutes long.

• Check the solution.To check, multiply the length of each show by the number of shows. 24 × 8 = 192.Since this product equals the number of minutes of programming without commercials, the answer checks.

8 192

16

32

32

24

0

1-7-47Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Solve the problem.Divide. Each show is 24 minutes long.

• Check the solution.To check, multiply the length of each show by the number of shows. 24 × 8 = 192.Since this product equals the number of minutes of programming without commercials, the answer checks.

8 192

16

32

32

24

0

1-7-48Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Solve the problem.Divide. Each show is 24 minutes long.

• Check the solution.To check, multiply the length of each show by the number of shows. 24 × 8 = 192.Since this product equals the number of minutes of programming without commercials, the answer checks.

8 192

16

32

32

24

0

1-7-49Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Solution: Part 2

• Solve the problem.Divide. Each show is 24 minutes long.

• Check the solution.To check, multiply the length of each show by the number of shows. 24 × 8 = 192.Since this product equals the number of minutes of programming without commercials, the answer checks.

8 192

16

32

32

24

0