Question

State sales tax S is directly proportional to retail price p . An item that sells for 172 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 )

Answer 1

`s(p) =(77p)/(1075)`

Explanation:

Given

s = sales tax

p = retail price

The variation is represented as:

`s\ \alpha\ p`

s = 12.32 when p = 172.

Required: Determine function s(p)

`s\ \alpha\ p`

Convert to equation

`s = kp`

Where k is the constant of variation.

Make k the subject

`k =(s)/(p)`

Substitute values for s and p

`k =(12.32)/(172)`

Multiply by 100/200

`k = (1232)/(17200)`

Simplify:

`k =(77)/(1075)`

To get the function, we substitute 77/1075 for k in:
`s = kp`

`s =(77)/(1075)p`

`s =(77p)/(1075)`

Express as a function

`s(p) =(77p)/(1075)`