3.8 Rates, Ratios and Percents

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3.8 Rates, Ratios and Percents

• We will use rates and ratios to model and solve
  real life world problems.
• We will use percents to model and solve real life
  problems.

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Using Rates and Ratios

• Rate of a per b is a/b.
• Unit rate -
• Think of miles per gallon or per hour.

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Interpreting Large Numbers

• Use unit rates to bring the numbers to something
  you can get a handle on.
• Total US spending. Remember 300 million people
  live in the US.

Clothing and shoes Restaurants Food at home Movie tickets
183 billion 190 billion 300 billion 10 billion
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Using collected data

• How many miles can you drive on 18 gallons of gas
  based on the data you collected?

of miles 290 242 196 237 184
of gallons 12.1 9.8 8.2 9.5 7.8
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Unit Analysis

• You are driving at 60 miles per hour. How many
  feet per minute are you driving?

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Converting money

• Currently you can buy .77 for 1. How many
  can you get with 4000?
• How many can you get with 4000?

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We will learn to solve proportions
Proportions
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Solving Proportions
 
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Applications of Proportions

• Read the problem and represent the unknown
  quantity by x.
• Set up a proportion by listing the given ratio on
  one side and the ratio with the unknown quantity
  on the other side.
• Make sure that similar values are in numerators
  and similar values are in the denominators.
• Drop units and apply the cross products
  principle.
• Solve for x and answer the question.

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Example of aligning a proportion correctly
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Example of aligning a proportion correctly

• Unwritten rule of local politics is that for
  every lawn sign you place you can count on 12
  votes. How many votes can someone who places 220
  lawn signs expect to receive?

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Solving a Direct Variation Problem

• A person works for 12/hr. The person works 15
  hours, how much money does he earn?