Chapter 3: Solving Equations

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Chapter 3 Solving Equations

• 3.4
• Ratio Proportion

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Vocabulary

• Ratio
• Comparison of two numbers by division
• Rate
• If a and b represent quantities in different
  units, then the ratio of a to b is a rate
• Unit Rate
• Rate with a denominator of 1

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Example 1

• The table gives prices for different sizes of the
  same brand of apple juice. Find the unit rate
  (cost per ounce) for each. Which has the lowest
  cost per ounce?

Price Volume
.72 16 oz
1.20 32 oz
1.60 64 oz
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Example 1a

• Main Street Florist sells two dozen roses for
  24.60. Flowers for You Florist sells six roses
  for 7.50. Find the unit rate for each. Which
  florist has the lower cost per rose?

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Example 2

• In 2004, Lance Armstrong won the Tour de France,
  completing the 3391 km course in about 83.6
  hours. Find Lances unit rate, which is his
  average speed. Write a rule to describe the
  distance he cycles d as a function of the time t
  he cycles. Cycling at his average speed, about
  how long would it take Lance to cycle 185 km?

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Example 2a

• Suppose you walk 2 miles in 35 minutes.
• Find the average walking speed. Write a rule to
  describe the distance d you walk as a function of
  the time t you walk.
• Use the function to find how far you would walk
  in an hour.

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Example 3

• A cheetah ran 300 feet in 2.92 seconds. What was
  the cheetahs average speed in miles per hour?

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Example 3a

• A sloth travels 0.15 miles per hour. Convert
  this speed to feet per minute.

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Proportions

• An equation that states that two ratios are equal

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Example 4

• Solve

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Example 4a

• Solve

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Example 4b

• Solve

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Example 4c

• Solve

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Cross Products of a Proportion

• If , then ad bc

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Example 5

• A box of cereal weighing 354 grams contains 20
  grams of fat. Find the number of grams of fat in
  the recommended serving size of 55 grams.

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Example 5a

• Solve

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Example 5b

• Solve

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Example 5c

• Solve

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Example 6

• Solve the proportion

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Example 6a

• Solve the proportion

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Example 6b

• Solve the proportion

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Example 6c

• Solve the proportion

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Homework

• P. 145
• 6, 8, 14, 16 46 even