Using Proportions to Solve Problems
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Using Proportions to Solve Problems

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Word Problems solved using Ratios and Proportions

Word Problems solved using Ratios and Proportions

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Using Proportions to Solve Problems Using Proportions to Solve Problems Presentation Transcript

  • Using Proportions to solve Problems
    Many application problems can be easily solved using proportions.
  • Ratio and Proportion
    A ratio is a comparison of two values expressed as a quotient
    Example: A class has 12 girls and 18 boys. The ratio of girls to boys is
    This ratio can also be expressed as an equivalent fraction
    A proportion is an equation stating that two ratios are equal.
    Example: =
  • Cross Products
    A test to verify that we have a true proportion is to check the cross products. In a true proportion, the cross products are equal:
    2 • 18 = 12 • 3
    36 = 36
    In this case, the cross products are equal, so we have a true proportion
    This feature of proportions is very useful in solving problems.
  • Example Proportion Problems
    Change 42 inches to feet
    FIND: number of feet
    FACTS: there are 12 inches in one foot
    FORMULA: we’ll set up a proportion
    (label the values to ensure the ratio is
    accurate on bothsides of the proportion)
    SOLVE: 12x = 42 (find cross products)
    x = 3.5 (solve for x)
    ANSWER: Result: 42 inches = 3.5 feet. Substitute that value in the original proportion and take cross products:
    (12)(3.5) = (42)(1)
    42 = 42
  • More Proportion Problems
    If 12 gallons of gas cost $26.68, how much will 15 gallons cost?
    FIND: cost of 15 gallons
    FACTS: 12 gallons cost $26.68
    FORMULA: set up a proportion and label the parts
    SOLVE: 12 x = 15 •26.68 (multiply cross products)
    12 x = 400.20
    x = 33.35 (solve for x)
    ANSWER: 15 gallons will cost $33.35. Substitute and check cross products: (15)(26.68) = (12)(33.35)
    400.20 = 400.20
  • More Proportion Problems
    Yogurt is on sale at 5 cartons for $3.00, how much will it cost for 12 cartons?
    FIND: the cost of 12 cartons of yogurt
    FACTS: 5 cartons cost $3
    FORMULA: create a proportion and label the parts
    SOLVE: 5x = 36 (multiply cross products)
    x = 7.20 (solve for x)
    ANSWER: 5 cartons will cost $7.20. To check, substitute and verify cross products: (5)(7.20) = (12)(3)
    36 = 36
  • More Proportion Problems
    John has a free throw average of 5 out of 8 attempts. At this rate, how many successful free throws would he be expected to make out of 200 attempts?
    FIND: number of successful free throws expected
    FACTS: he normally makes 5 out of 8
    FORMULA: create a proportion and label the parts
    SOLVE: 8x = 1000 (multiply cross products)
    x = 125 (solve for x)
    ANSWER: John would be expected to make about 125 out 200 free throws. Check by substituting and checking cross products.
  • Similar Triangles
    Two triangles are similar if their corresponding angles have the same measure. Corresponding sides of similar triangles are proportional.
    Thus, the following is true about the triangles pictured:
    FIND: the measure of side x
    FACTS: corresponding sides are proportional
    FORMULA: we can use either of the other two corresponding sides to create our proportion to solve
    SOLVE: 4x = 48
    x = 12
    ANSWER: The measure of the missing side is 12. We can substitute it in the original proportion to check.