2025 AHS PRELIMS P1 Q22

In Bakery \(A\), a chicken pie costs $2.50, an apple pie costs $2.00 and a taro pie costs $1.80. In Bakery \(B\), a chicken pie costs $0.30 less, an apple pie costs $0.20 more and a taro pie costs $0.10 more.

This information can be represented by the matrix \(X=\begin{pmatrix}2.5&-0.3\\2.0&0.2\\1.8&0.1\end{pmatrix}\).

1. Peter wants to buy 5 chicken, 4 apple and 2 taro pies. Jane wants to buy 4 chicken and 7 apple pies. Represent their purchases in a \(2\times3\) matrix \(Y\).[1]
2. Evaluate the matrix \(W=YX\).[2]
3. What does the last column of \(W\) represent?[1]
4. Find the amount that Peter and Jane should spend in Bakery \(B\).[1]