Question

A CD usually sells for $18.00. If the cD is 10% off, and sales tax is 8%, what is the total price of the CD, including tax?

Answer 1

The total price is $17.50 rounded to the nearest penny.

Explanation:

To find the total price we can use the following formula:

`p = (color(red)(c) - color(green)(d)) + ((color(red)(c) - color(green)(d)) xx color(blue)(t))`

Where:

`p` is the price paid
`color(red)(c)` is the cost of the CD at its usual price = `color(red)($18.00)`
`color(green)(d)` is the amount of the discount which we need to calculate.
`color(blue)(t)` is the tax rate = `color(blue)(8%)`

First, let's calculate the amount of the discount.

"Percent" or "%" means "out of 100" or "per 100", Therefore 10% can be written as `10/100`.

When dealing with percents the word "of" means "times" or "to multiply".

Putting this altogether we can write this equation and solve for `color(green)(d)`, the amount of the discount, while keeping the equation balanced:

`color(green)(d) = 10/100 xx $18.00`

`color(green)(d) = ($180.00)/100`

`color(green)(d) = $1.80`

We now have all the values to substitute into the equation for the total price:

`p = (color(red)($18.00) - color(green)($1.80)) + ((color(red)($18.00) - color(green)($1.80)) xx color(blue)(8%))`

`p = (color(red)($18.00) - color(green)($1.80)) + ((color(red)($18.00) - color(green)($1.80)) xx color(blue)(8/100))`

`p = $16.20 + (($16.20) xx color(blue)(8/100))`

`p = $16.20 + (($129.60)/100)`

`p = $16.20 + $1.30`

`p = $17.50`