Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 3.94$, before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $\$ 5.53$, before tax. Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of apples.
Use the fact that for $\mathrm { A } = \left[ \begin{array} { l l } 3 & 2 \ 4 & 3 \end{array} \right] , \mathrm { A } ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \ - 4 & 3 \end{array} \right]$.
A) $0.83 per pound
B) $0.74 per pound
C) $0.80 per pound
D) $0.87 per pound

Question

Quizplus · Accepted Answer

The correct answer is A.The matrix equation is:$$\begin{bmatrix} 3 & 2 \\ 4 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3.94 \\ 5.53 \end{bmatrix}$$where x is the price per pound of oranges and y is the price per pound of apples.Solving for X, we get:$$\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 & -2 \\ -4 & 3 \end{bmatrix} \begin{bmatrix} 3.94 \\ 5.53 \end{bmatrix} = \begin{bmatrix} 0.83 \\ 0.74 \end{bmatrix}$$Therefore, the price per pound of apples is $0.74.

Matt Bought 3 Pounds of Oranges and 2 Pounds of Apples