Luis wants to buy a skateboard that usually sells for $79.16. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%?

1 Answer
Feb 16, 2018

See a solution process below:

Explanation:

First, we need to determine the sales price of the skateboard. The formula for find the discounted prices is:

#s = r - (r * d)#

Where:

#s# is the sales price of the item: what we are solving for in this part of the problem.

#r# is the regular price of the item: $79.16 for this problem.

#d# is the discount rate: 12% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 12% can be written as #12/100#.

Substituting and calculating #s# gives:

#s = $79.16 - ($79.16 * 12/100)#

#s = $79.16 - ($949.92)/100#

#s = $79.16 - $9.4992#

#s = $69.6608#

#s = $69.66# rounded to the nearest cent.

Now we can find the total price of the item with tax included. The formula for this is:

#t = p + (p * r)

Where, this time:

#t# is the total price: what we are solving for in this problem.

#p# is the price of the item: it is the sales price of the item for this problem which is $69.66

#r# is the tax rate: 6.75% or, using the same rule as in the formula above: #6.75/100#

Substituting and calculating #t# gives:

#t = $69.66 + ($69.66 * 6.75/100)#

#t = $69.66 + ($470.205)/100#

#t = $69.66 + $4.70205#

#t = $74.36205#

#t = $74.36# rounded to the nearest cent.

Luis would pay a total cost (with the discount and after tax) of $74.36