Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 1 Whole Numbers

1-7-2 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 1.7 Solving Application Problems

1-7-3 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Key Words and Phrases for Solving Application Problems

1-7-4 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Steps for Solving Application Problems

1-7-5 Copyright © 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?

1-7-6 Copyright © 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.

1-7-7 Copyright © 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.

1-7-8 Copyright © 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.

1-7-9 Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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?

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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?

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

Copyright © 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 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

Copyright © 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 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

Copyright © 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 = 240 Since this sum is equal to the total minutes of programming, the solution checks.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.

Copyright © 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.