jmc

Letting $t$ equal the number of tickets sold in a single order, we get the following inequality: $$\begin{array}{rl}4200& <(70-(t-60))(t)\\ 4200& <(130-t)(t)\\ 4200& <130t-t^2\\ \Rightarrow t^2-130t+4200& <0\\ \Rightarrow (t-60)(t-70)& <0\end{array}$$Since the two roots of the left-hand side are 60 and 70, the inequality must change sign at these two points. For $t<60$, both factors of the inequality are negative, thus making it positive. For $60<t<70$, only $t-70$ is negative, so the inequality is negative. Finally, for $t>70$, both factors are positive, making the inequality positive once again. This tells us that the range of $t$ that will result in a profit greater than \4200$is$(60,70)$.Sincethenumberofticketspurchasedinoneordermustbeaninteger,thelargestnumberofticketswhichbringsaprofitgreaterthan$\$4200$ is $t=\boxed{69}$.