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