afford to pay for the car is actually lower. What price for the car can she actually
afford? How much sales tax would she then pay?We start with Formula 9.1.1, plugging in the values that we know:T P(1 r)
$21,900 P(1.0875)
To fi nd P, we divide both sides by 1.0875:
P $20,137.93.In fact, Ardana can only afford a car costing a little over $20,000. To fi nd the amount of
sales tax on this amount, we subtract $21,900 $20,137.92 $1,762.07.A word of warning is in order here, because it is easy to fall into a common mistake on
problems like this one. It is tempting to use the following incorrect reasoning: Since the tax
rate is 8.75%, just take 8.75% of the $21,900 and subtract. The problem with this approach
is that the tax rate is a percent of the before-tax price, not a percent of the after-tax total. Just
as with simple interest versus simple discount or markup vs. markdown, it is important to
be careful that, when using percents, we are use them as a percent of the right thing. Since
Ardana didn’t know the before-tax price, she can’t just take 8.75% of it, and so the formula
approach we used in this example is the only reasonable way to approach her problem.
Another similar situation sometimes arises for a business. Usually, businesses quote
their prices before tax, and then add the tax on. Sometimes, though, prices are quoted
including sales tax. This might be done as part of a sales promotion, or by a business where
most purchases are made in cash, and where, to avoid having to make so much change, it
is more convenient for final prices to be nice round numbers.Example 9.1.7 A souvenir shop sets all of its prices to include 6.75% sales tax. For
the month of June, sales totaled $16,739. How much sales tax is due on these sales?T P(1 r)
$16,379 P(1.0675)
P $15,343.33Since the P is the total price of the items sold before tax, the difference between this and the
total sales must be the tax. Therefore, the tax is $16,379 $15,343.33 $1,035.67.Sales Tax Tables (Optional)
You may occasionally see tables for calculating sales taxes. In the past, retailers would
often keep a chart next to the cash register so that completing a sale would require adding a
looked-up tax amount, which made for easier arithmetic than multiplication by a decimal.
An example is below:5% SALES TAX TABLE
AMOUNTS LESS THAN $1.00 AMOUNTS OVER $1.00
ADD TO AMOUNT FROM THE LEFT
FOR THE <$1.00 AMOUNT
If the Amount is: The Tax is: Dollars: Tax: Dollars: Tax:Less than $0.10 $0.00 $1 $0.05 $6 $0.30
$0.10 to $0.29 $0.01 $2 $0.10 $7 $0.35
$0.30 to $0.49 $0.02 $3 $0.15 $8 $0.40
$0.50 to $0.69 $0.03 $4 $0.20 $9 $0.45
$0.70 to $0.89 $0.04 $5 $0.25
$0.90 to $0.99 $0.05 For each $10, add $0.50 in tax.380 Chapter 9 Taxes