A customer wants to buy a pair of hiking boots

Sort out the question

The boots cost $85.75 at first. The store takes 15% off. Then a coupon takes 25% off the sale price. The sale price is the price after the first discount. Then 8.5% tax is added. You need the final cost to the nearest cent. A cent is $0.01, the second place after the decimal point.

Take off the 15% discount

You save 15%, so you pay 85%. That is 0.85 of the price.

$$\text{new price} = \text{price} \times \left(1 - \frac{p}{100}\right)$$

$$\text{new price} = 85.75 \times \left(1 - \frac{15}{100}\right) = 85.75 \times 0.85 = 72.8875$$

A price can’t have part of a cent, so round to two decimal places. The third digit is 7, which is 5 or more, so round up.

$$72.8875 \approx 72.89$$

The sign ≈ means about. The sale price is $72.89.

Take 25% off the sale price

The coupon takes 25% off $72.89, so you pay 75% of it.

$$72.89 \times 0.75 = 54.6675 \approx 54.67$$

The price is now $54.67. Watch out: take the coupon off the sale price, not the first price. Adding 15% and 25% to get 40% off $85.75 leads to $55.82, choice A.

Add the 8.5% tax

You pay the price plus 8.5% more, which is 108.5% of it.

$$\text{total} = \text{price} \times \left(1 + \frac{t}{100}\right)$$

$$\text{total} = 54.67 \times 1.085 = 59.31695 \approx 59.32$$

Watch out: 8.5% is a percent of the price, not $8.50. Adding $8.50 gives $63.17, choice D.

See why rounding each time matters

A store rounds to the cent after each step, as you just did. The test’s answer is worked the same way. Keep every digit and round only at the end, and you get this:

$$85.75 \times 0.85 \times 0.75 \times 1.085 = 59.3122\ldots \approx 59.31$$

That is $59.31, which is not a choice. The first two roundings each went up by a tiny part of a cent. That was just enough to push the total from $59.31 to $59.32. So here, round at each step, as a store would. So the answer is C, $59.32.