Digital PSAT Math Practice Question 273: Answer and Explanation

Question: 273

A customer orders food to be delivered from a restaurant. The cost of the food, including tax, is c. The total price, t, the customer pays upon delivery is given by the equation t = 1.2c + 2, which accounts for the cost of the food, a 20% tip on the food, and a $2 delivery fee. The restaurant doubles its delivery fee, and in response, the customer halves the percent of tip he pays. Which of the following expressions would represent the new total price the customer pays for food of cost c delivered from the restaurant?

• A. 1.2c + 2
• B. 1.1c + 4
• C. 0.6c + 4
• D. 1.4c + 2

Correct Answer: B

Explanation:

(B) The 2 in the original equation is an added constant, so it is the delivery fee. Doubling the delivery fee would make it a constant $4. Thus, you can narrow the answer down to choices (B) and (C) since the delivery fee will be the only constant (the cost of food and tip will depend on c). You can eliminate choice (C) as it is unlikely that the restaurant would allow the customer to pay only 0.6 or 60% of the cost of the food.

If you want to see where the correct answer, choice B, comes from, you could separate the original equation into t = c + 0.2c + 2, where c is the cost of the food, 0.2c is the 20% tip, and 2 is the delivery fee.

Thus, if the tip is halved, it will now be 10% of the cost of food, or 0.1c. If the delivery fee is doubled, it will now be 4 instead of 2. Therefore, the new equation will be t = c + 0.1c + 4 = 1.1c + 4, which matches choice (B).