A watch costs $75. It is 10% off, then 8% sales tax is added. What… Step by Step

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The question

Question: A watch costs $75.

It is 10% off, then 8% sales tax is added.

What is the final price?

1 Find the discount

Percent means out of 100.

So 10% is 10 divided by 100: 0.1.

The point moves 2 places to the left.

10% = 10 ÷ 100 = 0.1

The discount is 10% of $75.

"Of" means times: 0.1 times $75.

That is $7.50.

discount = 0.1 × $75 = $7.50

To multiply decimals: first 1 times 75, as whole numbers.

That is 75.

Then count the decimal places: 1.

So it is 7.5.

1 × 75 = 75

1 decimal places: 7.5

Careful!

We can't just take 8% from 10%.

The tax is on the sale price, not on $75.

Careful: not 10% − 8% = 2% off: $73.50 ✗

2 Take it off

A discount comes off the price.

$75 minus $7.50 is $67.50.

sale price = $75 − $7.50 = $67.50

3 Find the tax

Percent means out of 100.

So 8% is 8 divided by 100: 0.08.

The point moves 2 places to the left.

8% = 8 ÷ 100 = 0.08

The tax is 8% of $67.50.

"Of" means times: 0.08 times $67.50.

That is $5.40.

tax = 0.08 × $67.50 = $5.40

To multiply decimals: first 8 times 6750, as whole numbers.

That is 54000.

Then count the decimal places: 4.

So it is 5.4000.

8 × 6750 = 54000

4 decimal places: 5.4000

4 Add it on

The tax is added to the price.

$67.50 plus $5.40 is $72.90.

total = $67.50 + $5.40 = $72.90

So the final price is $72.90.

5 Check

Let's check another way: we pay 100% minus 10%: 90% of the price.

0.9 times $75 is $67.50.

100% − 10% = 90%: 0.9 × $75 = $67.50

Then: we pay 100% plus 8%: 108% of the price.

1.08 times $67.50 is $72.90.

The same.

So the answer is right!

100% + 8% = 108%: 1.08 × $67.50 = $72.90

Let's look back.

First: find the discount.

Then: take it off.

Then: find the tax.

Then: add it on.

Last: check.

Answer