A bicycle rental station charges by hour for the rental of its bicycles. On a particular week, the normal bicycles, children bicycles, and family bicycles were rented for 210 hours, 40 hours and \(x\) hours respectively on Saturday. On Sunday, the normal bicycles, children bicycles, and family bicycles were rented for 325 hours, 65 hours and 32 hours, respectively.
Represent the above information in a \(2\times3\) matrix \(P\).[1]
The charges for one hour's rental are $12 for a normal bicycle, $8 for a children bicycle and $40 for a family bicycle. Find, in terms of \(x\), the matrix \(Q=P\begin{pmatrix}12\\8\\40\end{pmatrix}\).[1]
Explain what each element in \(Q\) represents.[1]
The revenue from rental of family bicycles on that Saturday is equivalent to the revenue from the rental of children bicycles on that Sunday. Calculate the value of \(x\).[1]
In the following week, a special event was held near the bicycle rental station. The rental revenue increased by 25% and 50% compared to the previous Saturday and Sunday respectively. Using your answer in (d) and matrix multiplication only, calculate the revenue on Saturday and Sunday, respectively.[2]