A fruit vendor sells three types of fruit baskets A, B and C

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A fruit vendor sells three types of fruit baskets A, B and C. Basket A contains 2 apples, 1 orange and 3 bananas; basket B contains 1 apple, 3 oranges and 2 bananas; basket C contains 4 apples, 2 oranges and 1 banana. On a certain day the vendor sold 34 apples, 26 oranges and 29 bananas in total. If x, y and z denote the numbers of baskets A, B and C sold respectively, which of the following is the correct matrix equation representing the situation? (a)

\begin{pmatrix}2 & 4 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}34\\26\\29\end{pmatrix}

(b)

\begin{pmatrix}2 & 1 & 4 \\ 1 & 3 & 2 \\ 3 & 2 & 1\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}29\\34\\26\end{pmatrix}

(c)

\begin{pmatrix}2 & 1 & 4 \\ 1 & 3 & 2 \\ 3 & 2 & 1\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}34\\26\\29\end{pmatrix}

(d)

\begin{pmatrix}2 & 1 & 3 \\ 1 & 3 & 2 \\ 4 & 2 & 1\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}34\\26\\29\end{pmatrix}

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