Section

Concepts

1.5 Homework questions?

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Section

Concepts

1.5 Applications of Rational Equations and Proportions

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1. Solving Proportions2. Applications of Proportions

DEFINITION Proportion

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Section

Concepts

1.5 Solving Proportions

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Step 1 – Cross multiply

Step 2 – Set the cross products equal to each other

Step 3 – Solve the equation

Step 4 – Check your solution

Example 1 Solving a Proportion

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Example 2 Solving a Proportion

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Solve the proportion. 10 2

33b

Example 3 Solving a Proportion

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Solve the proportion. 2

1.9 38

x

Example 4 Solving a Proportion

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Solve the proportion. 2 1

4 6

w

w

Example 5 Solving a Proportion

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Solve the proportion. 8 5

9 1 3 2a a

Example 6 Solving a Proportion

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Solve the proportion for Vf .

i i

f f

V T

V T

Section

Concepts

1.5 Solving Proportion Applications

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Step 1 – Read the problem

Step 2 – Set up a proportionStep 3 – Make sure the units of measure are in the same order on each side

Step 4 – Solve the proportion

Step 5 – Check your solution

Example 7 Using a Proportion in an Application

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For a recent year, the population of Alabama was approximately 4.2 million. At that time, Alabama had seven representatives in the U.S. House of Representatives. In the same year, North Carolina had a population of approximately 7.2 million. If representation in the House is based on population in equal proportions for each state, how many representatives did North Carolina have?

ExampleSolution:

7 Using a Proportion in an Application

(continued)

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Example 8 Using a Proportion in an Application

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A university has a ratio of students to faculty of 105 to 2. If the student population at the university is 15,750, how many faculty members are needed?

Example 9 Using a Proportion in an Application

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Cooking oatmeal requires 1 cup of water for every ½ cup of oats. How many cups of water will be required for ¾ cup of oats?

Example 10 You Try

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a.

b.A certain fertilizer is applied at a rate of 6 pounds per 150 square feet. How many square feet can be fertilized with 20 pounds of fertilizer?

c.In Minneapolis, there were 30 homeless persons visible for every 1050 homeless in shelters. If the number of homeless visible on the street grew to 75, how many would you expect to find in shelters?

2 6

1 2 1x x

Example 10 You Try

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a. 2 6

1 2 1x x

Example 10 You Try

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b. A certain fertilizer is applied at a rate of 6 pounds per 150 square feet. How many square feet can be fertilized with 20 pounds of fertilizer?

Example 10 You Try

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c. In Minneapolis, there were 30 homeless persons visible for every 1050 homeless in shelters. If the number of homeless visible on the street grew to 75, how many would you expect to find in shelters?

Example 11 You Try Two More! – Set these up.

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a. Biologists catch, tag, and release 125 trout in a pond. Later, 200 trout are caught and checked for tags. Forty of these trout are found to have tags. Write a proportion to estimate the total trout population in the pond.

b. A health department estimates that 8 vials of a malaria serum will treat 100 people. At this rate, how many vials are needed to treat 175 people? Write a proportion.

Section

Concepts

1.5 Applications of Rational Equations and Proportions

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1. Solving Proportions2. Applications of Proportions