2000019304

Adam’s mom and Peter’s mom compete to see who can buy groceries cheaper. For summer weekend, they both want to buy butter, sugar, flour, and vanilla sugar and there are two stores available Aha and Praha. \[~\] The following tables show the quantity of items they both plan to buy and their prices in stores Aha and Praha. \[ \begin{array}{|c|c|c|c|c|} \hline &\begin{gathered}\text{Butter}\\\text{(kg)}\end{gathered} &\begin{gathered}\text{Sugar}\\\text{(kg)}\end{gathered} &\begin{gathered}\text{Flour}\\\text{(kg)}\end{gathered} &\begin{gathered}\text{Vanila sugar}\\\text{(number of pieces)}\end{gathered}\\\hline \text{Adam's mom}& 0.5& 2&1&8 \\\hline \text{Peter's mom}& 0.25 &2&2&5 \\\hline \end{array}\] \[ \begin{array}{|c|c|c|} \hline &\mathrm{Aha} & \mathrm{Praha}\\\hline \text{Butter (per }1\,\mathrm{kg)}& 119.6\,\mathrm{CZK}& 159.6\,\mathrm{CZK} \\\hline \text{Sugar (per }1\,\mathrm{kg)} & 12.5\,\mathrm{CZK}& 9.9\,\mathrm{CZK} \\\hline \text{Flour (per }1\,\mathrm{kg)} & 10.9\,\mathrm{CZK} & 9.5\,\mathrm{CZK} \\\hline \text{Vanilla sugar (per } \mathrm{piece)} & 5.9\,\mathrm{CZK} & 5.1\,\mathrm{CZK} \\\hline \end{array}\] What follows from the next product of the two matrices? \[ \left (\array{ 0.5& 2 & 1 & 8\cr 0.25& 2 & 2 & 5\cr } \right ) \cdot \left (\array{ 119.6& 159.6 \cr 12.5& 9.9 \cr 10.9& 9.5 \cr 5.9& 5.1 \cr } \right ) = \left (\array{ 142.9& 149.9\cr 106.2& 104.2 \cr } \right ) \]