Loaves baked in a six-day week

Loaves baked in a six-day week

Secondary 4
4 marks

A bakery bakes white and wholemeal loaves for two outlets. It bakes the numbers in matrix \(P\) on each weekday, Monday to Friday, and the numbers in matrix \(Q\) on Saturday. It is closed on Sunday.

\(P=\begin{pmatrix}40&35\\ 25&30\end{pmatrix}\qquad Q=\begin{pmatrix}55&60\\ 30&45\end{pmatrix}\)

In both matrices the rows are white, wholemeal and the columns are Outlet 1, Outlet 2.

  1. Evaluate \(5P\).[1]
  2. Evaluate \(5P+Q\).[2]
  3. Explain what the entry in row 1, column 2 of \(5P+Q\) represents.[1]

Solution:

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Answer:(a) \(\begin{pmatrix}200&175\\ 125&150\end{pmatrix}\) (b) \(\begin{pmatrix}255&235\\ 155&195\end{pmatrix}\) (c) 235 white loaves baked for Outlet 2 in one week

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