Variation and Proportion

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Variation and Proportion

• Direct Proportion

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The formula for direct variation can be written
as ykx where k is called the constant of
variation.

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

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ProblemFind an equation of direct variation
where y varies directly as x. One pair of values
is y 7 when x 35.

• Write the equation y kx y kx
• Substitute for x and y 7 k(35)
• Solve for k 7/35 k, or k 1/5
• Rewrite the equation with k y 1/5x
• as the constant

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ProblemThe cost of operating a TV varies
directly as the number (n) of hours it is in
operation. It costs 14.00 to operate a standard
size color TV continuously for 30 days.

• y cost x number of hours
• y kx
• 14 k(30)
• 14/30 k, or k 7/15
• Equation
• y 7/15x

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Practice Problems Answers

• y 28 when x 7
• Equation y 4x
• y 30 when x 8
• Equation y 15/4x
• y 400 when x 125
• Equation y 16/5x
• y 630 when x 175
• Equation y 18/5x

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Practice Problems Answers (Continued)

• The number (b) of bolts a machine can make varies
  directly as the time it operates. It can make
  6578 bolts in 2 hours. How many bolts can it make
  in 5 hours?
• Set up a proportion
• 6578/2 x/5
• x 16445