Nancy is shopping at a supermarket. She wants to buy a liquid soap bottle that has a discount of 15 percent on its retail price. A sales tax of 7 percent is added to the price of the soap after the discount. Which of the following expressions represents the total price of buying a liquid soap bottle with retail price of 𝑥 dollars? A) 𝑥 plus 0.07𝑥 minus 0.15𝑥. B) 1.07 times 0.15𝑥. C) 0.07 times 𝑥 minus 0.15𝑥. Or D) 1.07 times 0.85𝑥.
We know that Nancy gets a discount of 15 percent. For a 15 percent discount, you pay 85 percent of the original cost. For a sales tax of 7 percent, you pay 107 percent. If we break down the 85 percent, it’s the 100 percent of the original price with 15 percent taken off. 100 minus 15 equals 85. If we break down the sales tax, you pay 100 percent of the cost of the items plus a 7 percent tax on top of that.
For this liquid soap, the first thing that happens is the discount is taken off. And so, we write 85 percent as a decimal 0.85 and we multiply that by 𝑥, the original cost of the soap. This is now the cost of the soap with the discount. And we need to calculate sales tax on this amount. We need to multiply it by 1.07. 1.07 is the way that we write 107 percent in decimal form. An expression for calculating the cost of the liquid soap after the discount and then sales tax would be 1.07 times 0.85𝑥, which is option D.
Before we move on, let’s consider why the other three options don’t work. Option A is actually very close. 𝑥 minus 0.15𝑥 is the cost of the soap after the discount. The problem comes in with the term 0.07𝑥. Option A is calculating the sales tax based on the original price and not on the discounted price. What about option B? Option B has multiplied 0.15 times 𝑥. It’s found the discount for the bottle of soap and then calculated the sales tax on the discount.
And what about option C? Option C has also calculated correctly the discount. 𝑥 minus 0.15𝑥 does tell us how much the bottle of soap costs after the discount. But multiplying this by 0.07 only tells us how much sales tax that Nancy should pay. It does not tell us the total cost that Nancy would have to pay. Out of these expressions, only expression D correctly calculates the price Nancy would pay with a 15 percent discount and a 7 percent sales tax on the soap bottle.