PSAT Math Multiple-Choice Question 126: Answer and Explanation

Question: 126

The total cost of the frisbees and hats is $72, and the cost of two hats and a frisbee is $14.50. What is the cost of a frisbee?

• A. $3.22
• B. $4.50
• C. $5.50
• D. $5.78

Correct Answer: C

Explanation:

C

The question asks for the cost of a frisbee. Since the question asks for a specific amount, plugging in the answers is an option. However, there is a lot of information about the cost of hats and frisbees, so this may get confusing. Instead, start by translating English to math, then solve the resulting system for the price of a frisbee. Let f represent the cost of a frisbee and h represent the cost of a hat. The question says that the total cost of the frisbees and hats is $72, so 5h + 9f = $72. The question also says that the cost of two hats and a frisbee is $14.50, so 2h + f = $14.50. Next, solve for the price of one frisbee, or the value of f One way to solve is to stack the equations and add to eliminate the price of hats. Multiply the equations so the coefficients on the price of hats are the same but with opposite signs. Multiply the first equation by 2 to get 10h + 18f = $144.00. Multiply the second equation by -5 to get -10h - 5f= -$72.50. Stack and add the equations.

Divide both sides by 13 to get f= $5.50. The correct answer is (C).