1. 6
Ratio, Proportion, and Line/Angle/Triangle Relationships

2. R.1 Fractions
6.4 Problem Solving with Proportions
Objectives
Use proportions to solve application problems.

3. 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.

4. Use proportions to solve application problems.
(continued)
Example
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.

5. Use proportions to solve application problems.
Example
(continued)
Step 4 Solve the equation.
Ignore the units while finding the cross
products.

6. 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.

7. 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.

8. 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.

9. Use proportions to solve application problems.
Example
(continued)
Step 4 Solve the equation.

10. 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 people, is between 1600 and 3200, so it is reasonable.