Question

State sales tax S is directly proportional to retail price p. An item that sells for 168 dollars has a sales tax of 10.22 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 290 dollars purchase. Round to the nearest cent. The sales tax on a 290 dollar purchase is $

Answer 1

Mathematical model:

`S(p)=(10.22)/(168)p`

The sales tax on a 290 dollar purchase is $17.6

Step-by-step explanation:

We're told that sales tax(S) is directly proportional to retail price(p), this can be represented mathematically as;

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

where k = the proportionality constant

We're also told that when p = $168, S = $10.22, we can solve for k by substituting these values into our equation as see below;

`\begin{gathered} 10.22=k*168 \\ k=(10.22)/(168) \end{gathered}`

So the mathematical model can be written as;

`S(p)=(10.22)/(168)p`

When p = $290, we can solve for S as shown below;

`S(290)=(10.22)/(168)(290)=(2963.8)/(168)=\text{ \$17.}6`