copyright © 2008 pearson addison-wesley. all rights reserved. chapter 1 whole numbers
TRANSCRIPT
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
1-7-4Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
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