Question

The tailor determines that the cost of material varies directly with the amount of material. The cost is $42 for 14 yards of material. What is the cost for 70 yards of material?

Answer 1

`the \: cost \: for \: 70 \: yards \: of \: material \: is : \\ \: \$210.`

Explanation:

`let \: the \: cost \: of \: material \: be \to \: c_(m) \\ let \: the \: amount \: of \: material \: be \to \: a_(m) \\ then \: the \: expression \: is: \\ c_(m) \: \alpha \:a_(m) \\ c_(m) \: = k a_(m) \\ if \: c_(m) = 42 \: and \:a_(m) = 14 \\ then \: \to \\ k = (c_(m) )/(a_(m)) = (42)/(14) \\ k = 3 \to \: this \: is \: the \: variation \: constant. \\ when \: a_(m) = 70 : \: then \to \\ c_(m) = k a_(m) = 3 * 70 \\ \boxed{ c_(m) = \: 210}`

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