6.4 Problem Solving with Proportions Chapter 6 Ratio, Proportion, and Line/Angle/Triangle Relationships

6.4 Problem Solving with Proportions Objectives Use proportions to solve application problems. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Objective 1: Use proportions to solve application problems. Example Mike’s car can travel 163 miles on 6.4 gallons of gas. How far can it travel on a full tank of 14 gallons of gas? Round to the nearest mile. Step 1 Read the problem. Unknown: miles traveled on 14 gallons of gas Known: 163 miles traveled on 6.4 gallons of gas Step 2 Assign a variable. Let x be the number of miles traveled on 14 gallons. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 4

Objective 1: Use proportions to solve application problems. Example (continued) Step 3 Write an equation. Decide what is being compared. This problem compares miles to gallons. Write the two rates described in the problem. Be sure that both rates compare miles to gallons in the same order. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 5

Objective 1: Use proportions to solve application problems. Example (continued) Step 4 Solve the equation. Ignore the units while finding the cross products. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 6

Objective 1: Use proportions to solve application problems. Example (continued) Step 5 State the answer Mike’s car can travel 357 miles, rounded to the nearest mile, on a full tank of gas. Step 6 Check the answer The car traveled 163 miles on 6.4 gallons of gas; 14 gallons is a little more than twice as much gas, so the car should travel a little more than twice as far. The solution, 357 miles, is a little more than the estimate of 326 miles, so it is reasonable. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 7

Objective 1: Use proportions to solve application problems. Example A newspaper report says that 7 out of 10 people surveyed watch the news on TV. At that rate, how many of the 3200 people in town would you expect to watch the news? Step 1 Read the problem. Unknown: how many people in town are expected to watch the news on TV Known: 7 out of 10 people surveyed watched the news on TV. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 8

Objective 1: Use proportions to solve application problems. Example (continued) Step 2 Assign a variable. Let x be the number of people in town who watch the news on TV Step 3 Write an equation. You are comparing people who watch the news to people surveyed. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 9

Objective 1: Use proportions to solve application problems. Example (continued) Step 4 Solve the equation. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 10

Objective 1: Use proportions to solve application problems. Example (continued) Step 5 State the answer You would expect 2240 people in town to watch the news on TV. Step 6 Check the answer 7 out of 10 people is more than half the people, but less than all the people. Half of the 3200 people in town is 1600, so between 1600 and 3200 people would be expected to watch the news on TV. 2240 people, is between 1600 and 3200, so it is reasonable. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 11