MAT 150 Unit 9

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MAT 150 Unit 9

• Ch 8 1 and 8 2
• Using Proportions to Solve Linear Equations and
  Direct Variation

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Section 8 1 Using Proportions to Solve Linear
Equations

• Proportion equations equations where each side
  is ONE and only ONE fraction
• Example
• N is to 5 as 1 is to 12
• N5 112
• N 1
• 5 12

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Section 8 1 Using Proportions to Solve Linear
Equations

• N 1
• 5 12
• To solve cross multiply
• N 1
• 5 12
• N(12) 5(1)
• 12N 5
• N 5/12

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Section 8 1 Using Proportions to Solve Linear
Equations

• X 9
• 4 6
• 6x 36
• x 6
• X 2 3
• X 8 5
• 5(x 2) 3(x 8)
• 5x 10 3x 24
• 2x 10 24
• 2x 34
• x 17

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Section 8 1 Using Proportions to Solve Linear
Equations

• BE CAREFUL using cross multiplication only works
  when both sides are SINGLE fractions (one term)!
• Not a proportion
• X 5 9 (solve by multiplying by CD)
• 2 4
• Proportion
• X 5 9 (solve by cross multiplying)
• 2 4

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Section 8 2 Direct Variation

• Solving Direct Variation problems
• Establish 2 pairs of related data
• Write 1 pair as the numerators
• Write the other pair as the denominators
• Form a proportion and solve
• Find the cost of 10 apples if 4 apples can be
  purchased for 1.
• Pair 1 4 apples cost 1
• pair 2 10 apples cost x dollars
• 4 1
• 10 x
• 4x 10
• x 2.50

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Section 8 2 Direct Variation

• A truck travels 102 mi. on 6 gallons of gas, how
  far will it go on 30 gallons?
• Pair 1 102 mi. on 6 gallons
• pair 2 x mi. on 30 gallons
• 102 6
• x 30
• 6x 3060
• x 510 miles
• NOTE when establishing pairs keep the same order
  of the units of measure (ie. mi gal and mi
  gal)

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Section 8 2 Direct Variation

• Constant of variation (aka unit cost or cost of
  one)
• K x/y where x and y are the known information
• Example
• A 15 oz. Box of cereal cost 2.29. Find the
  constant of variation (unit cost) per ounce.
• K x/y
• K cost per ounce or cost/oz
• K 2.29/15 0.1527

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Section 8 2 Direct Variation

• Which is a better buy, the 15 oz. Box of cereal
  at 2.29 or 36 oz at 4.89?
• 15oz. Was 2.29/15 or 0.1527
• The 36 oz is
• k 4.89/36 0.1358
• So the 36 oz. Box would be a better buy.