PSAT Math Multiple-Choice Question 483: Answer and Explanation

Question: 483

Bill can purchase eight hockey pucks and two water bottles for $22 or twelve hockey pucks and ten water bottles for $54. For his team’s hockey practice, Bill needs sixteen water bottles. How much will it cost for Bill to purchase the sixteen water bottles given the above costs?

• A. $20
• B. $22
• C. $48
• D. $54

Correct Answer: C

Explanation:

C

The question asks for the cost of a certain number of items. The price of the item is unknown, so begin by translating the English to math in bite-sized pieces. The cost of one hockey puck can be represented as p and the cost of one water bottle as w. The question states that Bill can purchase eight hockey pucks and two water bottles for $22, so this can be represented as 8p + 2w = 22. It also says that he can buy twelve hockey pucks and ten water bottles for $54, which can be represented as 12p + 10w = 54. The question asks about the cost of water bottles, so solve the system for w. To do so, get the first equation, 8p + 2w = 22, in terms of p and then substitute that into the second equation. Start by subtracting 2w from both sides to get 8p = 22 – 2w, then divide both sides by 8 to get or . Substitute into 12p + 10w = 54 to get . Distribute to get (33 – 3w) + 10w = 54, then combine like terms to get 33 + 7w = 54. Subtract 33 from both sides to get 7w = 21. Divide both sides by 7 to get w = 3. This is the cost of one water bottle, and the question asks for the cost of 16 water bottles, so multiply 16 by $3 to get $48. The correct answer is (C).