Variation and Proportion

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Variation and Proportion

• Indirect Proportion

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The formula for indirect variation can be written
as yk/x where k is called the constant of
variation.We can follow the same steps from
direct variation!! ?

• The steps to follow to solve a problem with
  indirect variation
• Write the equation y k/x
• Substitute for x and y
• Solve for k
• Rewrite the equation with k as the constant

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ProblemFind an equation of indirect variation
where y varies indirectly as x. One pair of
values is y 145 when x .8.

• Write the equation y k/x y k/x
• Substitute for x and y 145 k/.8
• Solve for k 145(.8) k, or k 116
• Rewrite the equation with k y 116/x
• as the constant

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ProblemThe time (t) required to do a certain
job varies inversely as the number (n) of people
working (assuming all work at the same rate). It
takes 4 hours for 20 people to wash and wax the
floors in a building. Find the equation of
variation.

• y time x number of people
• y k/x
• 4 k/20
• 420 k, or k 80
• Equation
• y 80/x

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Practice Problems Answers

• y 25 when x 3
• Equation y 75/x
• y 45 when x 2
• Equation y 90/x
• y 80 when x .7
• Equation y 56/x
• y .8 when x 4
• Equation y 3.2/x

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Practice Problems Answers (Continued)

• It takes 16 hours for 2 people to resurface a gym
  floor. How long would it take 6 people to do the
  job?
• Write the equation y k/x y k/x
• Substitute for x and y 16 k/2
• Solve for k 16(2) k, or k 32
• Rewrite the equation with k y 32/x
• as the constant