Use matrices to find the cost of 1 kg of bananas

Question

Claire and Dale shopped at the same store.

Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22

Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33

Use matrices to find the cost of 1 kg of bananas

Answer 1

The following might be helpful to get you going in the right direction:

$$ \begin{bmatrix} 5 & 2 \\ 4 & 6 \\ \end{bmatrix} \begin{bmatrix} c_{apples} \\ c_{bananas} \\ \end{bmatrix} = \begin{bmatrix} 22 \\ 32 \\ \end{bmatrix} $$

where $c_{apples}$ is the cost per kg of apples, and $c_{bananas}$ is the cost per kg of bananas. (Please note: this is in the form of $A\mathbf{x}=\mathbf{b}$). Both of these are unknown, so you can use matrix methods to find the solution:

$$ \mathbf{x}= \begin{bmatrix} c_{apples} \\ c_{bananas} \\ \end{bmatrix} $$.

I hope this helps.