PSAT Math Multiple-Choice Question 21: Answer and Explanation

Question: 21

A group of students sells different types of cookies at a bake sale to raise funds for a school trip. When the students sell two snickerdoodle cookies, s, and seven cinnamon cookies, c, they raise $14.00. When the students sell eight snickerdoodle cookies and three cinnamon cookies, they raise $17.50. Assuming the price per cookie does not change, which of the following equations represents a sale the students could make during the fundraiser?

• A. 2s + 3c = $8.00
• B. 4s + 6c = $16.25
• C. 6s + 5c = $17.36
• D. 8s + 7c = $24.50

Correct Answer: C

Explanation:

C

The question asks which equation represents a sale the students could make during the fundraiser. Translate the English into math to create a system of equations, and then solve the equations to find the prices for snickerdoodle and cinnamon cookies. The first sale described can be written as 2s + 7c = 14.00. The second sale described can be written as 8s + 3c = 17.50. Multiply the first equation by -4 to get -8s - 28c = -56.00, stack the equations, and add.

Divide both sides by -25 to get c = 1.54. Plug in the value for c into the original first equation to get 2s + 7(1.54) = 14.00. Subtract 7(1.54) from both sides, and divide by 2 to get s = 1.61. Plug the values for s and c into the answer choices to find an equation that works. 2(1.61) + 3(1.54) does not equal 8, so eliminate (A). 4(1.61) + 6(1.54) does not equal 16.25, so eliminate (B). 6(1.61) + 5(1.54) does equal 17.36. The correct answer is (C).