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?
(A) 29
(D) 28
(B) 30
(C) 27
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 twentyfifth 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?
(A) 29
(B) 30
(D) 28
(E) 31

## Solution

For Raymonde's first twenty five transactions, each set of five would cost $.50+.45+3(.60)=2.75$. After 25 transactions, her total cost would be $\$ 13.75$. In order to exceed $\$ 15.95$, she would have to spend \$2.20. In order to minimize the number of transactions, she would use Autodebit four times. In total, the number of transactions would be $25+4=29$.