Question 8 • Advanced Algebra: Concepts and Connections
Jeremy’s fruit stand sells peaches and watermelons. In the first hour the fruit stand is open, 12 bushels of peaches and 5 watermelons are sold for a total of 150 dollars In the second hour, 15 bushels of peaches and 8 watermelons are sold for a total of 198 dollars A bushel of peaches costs p dollars, and a watermelon costs w dollars. Which matrix equation represents the situation?
Answer
A
the 2 by 2 matrix row 1, 5 12 row 2, 8 15 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
B
the 2 by 2 matrix row 1, 12 5 row 2, 15 8 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
C
the 2 by 2 matrix row 1, 5 8 row 2, 12 15 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
D
the 2 by 2 matrix row 1, 12 15 row 2, 5 8 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
Explanation
Let p be the price per bushel of peaches and w the price of a watermelon. The first hour gives 12p + 5w = 150, and the second hour gives 15p + 8w = 198. These coefficients form the rows [12, 5] and [15, 8], so the matrix equation is choice B.
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