Question

State sales tax S is directly proportional to retail price p. An item that sells for 164 dollars has a sales tax of 12.32 dollars. Find a mathematical model that gives the amount of sales tax S in terms of the retail price p. Function: S(p) What is the sales tax on a 310 dollars purchase. Round to the nearest cent. The sales tax on a 310 dollar purchase is $ Question Help: D Video Submit Question

Answer 1

Mathematical model: S(p) = 0.08p

`S(p)=(12.32p)/(164)`

S(310) = $23.3

Step-by-step explanation:

We're told from the question that sales tax, S, is directly proportional to retail price, p. This can be represented mathematically as seen below;

`\begin{gathered} S\propto p \\ S=kp \end{gathered}`

where k = the constant of proportionality.

From the question, we're also told that when p = $164, S = $12.32.

Substituting the above values into our equation, we'll have;

`\begin{gathered} 12.32=k*164 \\ k=(12.32)/(164) \end{gathered}`

So our mathematical model can be represented as;

`S(p)=(12.32p)/(164)`

Therefore, when p = $310, we can solve for S as seen below;

`\begin{gathered} S(310)=0.08*310 \\ S(310)=\text{ \$23.}3 \end{gathered}`