The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $32 item is $33.60 , what is the total cost on a $55 item

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12-12-2017
Mathematics

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The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $32 item is $33.60 , what is the total cost on a $55 item

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2017-12-20T12:03:35+01:00

Let the total cost of the item be represented by C and the price be represented by P, then given that the total cost of an item including sales tax is directly proportional to its price, thus

[tex]C\propto P \\ \\ \Rightarrow C=kP[/tex]

where k is a constant.

Given that the total cost of a $32 item is $33.60, thus

[tex]33.60=32k \\ \\ \Rightarrow k= \frac{33.60}{32} =1.05[/tex]

Therefore, the total cost on a $55 item is given by

[tex]C=1.05\times55=\$57.75[/tex]