8.1.17 Calculating Sales Tax

Notepad iconActivity: Expensive Sales Tax

(a) Sabrina was visiting California, and bought a pair of sneakers with a ticket price of $69. The California sales tax rate at the time was 8.25%. First, without using a calculator, give an estimate of what the shoes cost in all. Afterward, find the exact price of her purchase.

Calculator icon The calculator can be accessed on the left-hand side bar under Toolkit.

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Comment

It does not matter if you figure the sales tax as an estimated 10% (rounded up very roughly) or 8% (rounded down to the closest percent). Working with 10% clearly is much easier. The $69 rounds to $70, and since 10% of $70 is $7 (just divide 70 by 10), the total comes out to less than $77.

Now, use the exact numbers to find the actual purchase price Sabrina paid. Pay close attention to your decimal places, as you are converting a one-digit percentage to a decimal.

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Answer

(a) 8.25% of $69 is equation left hand side 0.0825 multiplication dollar times 69 almost equals right hand side dollar times 5.69 (rounded to the closest cent) The total price was dollar 69 postfix plus dollar 5.69 equals dollar 74.69.

You may also have calculated it like this:equation left hand side 1.0825 multiplication dollar times 69 almost equals right hand side dollar times 74.69.

(b) [ Sabrina was fortunate. If you travel to England now, 20% VAT is added to all purchases. ] When Sabrina traveled to Europe in 2010, she was amazed to see that England has a 17.5% sales tax, which is called VAT (value added tax). In London, she bought a pair of boots that were £26 before tax. After calculating a rough estimate of sales tax and final purchase amount, can you find the exact sales tax in your head using mental strategies from chapter 2? Then find the exact purchase amount.

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Comment

Make an estimate first. 20% of £30 is approximately two postfix multiplication pound three equals pound six. Since we rounded up, we expect the VAT to be less than £6.

For the mental approach, think about breaking the VAT of 17.5% down into 17.5 percent equals 10 percent prefix plus of five percent prefix plus of 2.5 percent. Do you see that each of these partial percentages is half of the last? You also know how to find 10% of an amount. Use these strategies to do your mental math.

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Answer

(b) 10% of £26 is £2.60.

5% of £26 is £1.30 (half of £2.60).

2.5% of £26 is £0.65 (half of £1.30).

Therefore, 17.5% of £26 is pound 2.60 postfix plus pound 1.30 postfix plus pound 0.65 equals pound 4.55, which is less than £6, and thus reasonable when compared to our estimate.

The final price is the original cost plus the VAT is pound 26 postfix plus pound 4.55 equals pound 30.55.

The corresponding amount in U.S. dollars depends on the current exchange rate. In 2010, the exchange rate was about $1.60 per British pound. This would make the boots approximately £equation left hand side 30.55 multiplication 1.6 equals right hand side dollar times 48.88. We’ll look at more conversions like this in Unit 9.

8.1.18 Leaving a Tip