Tickets to a carnival cost \(\$10\) for adults (A), \(\$8\) for senior citizens (S) and \(\$5\) for children (C). This information can be represented by the matrix \(\mathbf Q=\begin{pmatrix}10\\8\\5\end{pmatrix}\).
68 adults, 15 senior citizens and 70 children bought tickets through ticket counter. 72 adults and \(x\) children bought tickets online. Represent this information in a \(2\times3\) matrix \(\mathbf P\), with columns A, S and C.[1]
Find the matrix \(\mathbf R\), in terms of \(x\) such that \(\mathbf R=\mathbf P\mathbf Q\).[2]
Explain what each element in matrix \(\mathbf R\) represents.[1]
The total amount of money collected from the ticket counter is less than that from the online sales. Find the least value of \(x\).[2]