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?

1 Answer
Jan 4, 2017

Answer:

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#