1999 Gauss 8 Problem 24

Raymonde's financial institution publishes a list of service charges as shown in the table. For her first twenty five transactions, she uses Autodebit three times as often as she writes cheques. She also writes as many cheques as she makes cash withdrawals. After her twenty- fifth transaction, she begins to make single transactions. What is the smallest number of transactions she needs to make so that her monthly service charges will exceed the \$15.95 'all-in-one' fee?

\begin{array}{lc} \text{Service Fee per Item} & \\ \hline \text{Cheque} & \$0.50 \\ \text{Autodebit} & \$0.60 \\ \text{Cash Withdrawal} & \$0.45 \\ \end{array}

'All-in-one' fee is \$15.95

\textbf{(A)}\ 29\quad \textbf{(B)}\ 30\quad \textbf{(C)}\ 27\quad \textbf{(D)}\ 28\quad \textbf{(E)}\ 31

If there are no answer choices shown, enter a numerical answer.

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