SAT Math Multiple Choice Question 806: Answer and Explanation

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Question: 806

11. Tricia manages a health bar and wants to add a new fruit-and-protein smoothie to themenu. To decide on the first new flavor she plans to offer, Tricia sold trial-sizedbanana smoothies and kiwi smoothies. She charged $2 for a banana smoothie and $2.50for a kiwi smoothie, and she sold 40 in all, totaling $87. How much more money didTricia make on the banana smoothies than the kiwi smoothies?

  • A. $12
  • B. $17
  • C. $26
  • D. $52

Correct Answer: B



Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: When you're given two types of information, write and solve a system of equations to answer the question. Before selecting your answer, be sure to check that you answered the right question.

Getting to the Answer: Let b and k represent the number of banana and kiwi smoothies sold. Tricia sold 40 smoothies in all, so b + k = 40. She sold banana smoothies for $2 each and kiwi smoothies for $2.50 each for a total of $87, so 2b + 2.5k = 87. Use either combination (elimination) or substitution to solve for b and k. To use substitution, solve the first equation for either variable (b + k = 40 → b = 40 - k) and substitute the result into the second equation:

From before, b = 40 - k → 40 - 14 = 26, so Tricia sold 26 banana smoothies and 14 kiwi smoothies. Don't stop yet and don't fall for the trap answer, which is A. The question asks how much more money was made on the banana smoothies than the kiwi smoothies (not how many more banana smoothies were sold than kiwi smoothies). Tricia made $2 × 26 = $52 on the banana smoothies and $2.50 × 14 = $35 on the kiwi flavor, for a difference of 52 - 35 = $17. (B) is the correct answer.

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