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]
