Question

Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?

Answer 1

To calculate the total purchase price for Martin Pincher, we need to calculate the total amount of taxes he must pay and then add the purchase price of the items.

Let's start by calculating the taxes.

State Tax:

State Tax = 0.05 x (28.61+23.27+7.96)

State Tax = 0.05 x 59.84

State Tax = 2.99

County Tax:

County Tax = 0.005 x (28.61+23.27+7.96)

County Tax = 0.005 x 59.84

County Tax = 0.30

City Tax:

City Tax = 0.025 x (28.61+23.27+7.96)

City Tax = 0.025 x 59.84

City Tax = 1.50

Total taxes = 2.99 + 0.30 + 1.50

Total taxes = 4.79

Now let's calculate the total purchase price.

Total purchase price = 28.61+23.27+7.96 + 4.79

Total purchase price = 64.63

Answer 2

$64.63

Explanation:

You want to know the total with tax of purchases of $28.61, 23.27, and 7.96 when they are subject to taxes of 5%, 0.5% and 2.5%.

Total sale

The sum of the individual prices is subject to tax that is the sum of the individual tax rates. The tax rate sum is ...

5% +0.5% +2.5% = 8%

Then the multiplier of the price is ...

total = subtotal × (1 +8%) = 1.08×subtotal

A calculator can do all the computations at once, so we don't actually need to know the subtotals in order to find the total sale amount.

(28.61 +23.27 +7.96) × 1.08 = 64.6272

The tax is generally rounded to the nearest cent, so ...

the total purchase price is $64.63.

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Additional comment

In the days before smart cash registers, the amount of sales tax was found by looking in a table supplied by the tax authority. It was always the same for any given purchase amount.

These days, the tax may be computed on the fly in such a way that the total tax collected is as near as possible to the total tax that needs to be collected.

That means a hundred instances of this purchase might have a total price of $64.63 for 72 of them, and $64.62 for the remaining 28 of them. That way, the total of the 100 sales would be $6462.72 and exactly the right amount of tax will have been collected. (At least one pizza chain collects tax this way.)