"Who are these old ladies, aunty?" asked my nephew, Danny, pointing to a picture in the family photo album.
 

"Those ‘old ladies’ were my two favorite aunties, Danny. Their names were Bucky and Nannie." I said, smiling, as I looked at their pictures. "This was taken at my tenth birthday party, which we celebrated at my grandmother’s house that year. And, by the way, they were about as old as I am now!"
 

"Oh, wow!" said my niece, Gina. "How can you remember back that far?"

"Hey, its not that far back," laughed Barney, my other nephew. "Why did you remember that birthday, Aunty? Did something special happen?"

"I’ll say it did!" I recalled. "That’s the year my rich auntys were visiting and they gave me some birthday money. I didn’t have much money in those days so I remember it well!"

"How much did they give you?" asked Gina. "Was it a lot?"
 

"Well, I remember my aunt Bucky opening up her big, black purse and pulling out a shiny, silver dollar. Then aunt Nannie reached in her little red coin purse and pulled out a shiny little dime. They told me that since I was ten years old, it was time for me to make 'THE MONEY DECISION.'

"What decision was that?" asked Danny.

"That’s what I wanted to know too, Danny," I said.
 

The auntys had explained that I had to make a choice. I could choose the silver dollar or the dime for my birthday money. But I should choose wisely.

For if I chose the silver dollar, each year after that until they both died, they would send me one more silver dollar on my birthday than they had sent the year before. However, if I chose the dime, each year after that until they both died, they would send me twice as much money as they had sent the year before.
 

"So, if you chose the dollar you would get two dollars on your eleventh birthday, but if you chose the dime, you would only get twenty cents on your eleventh birthday?" asked Gina.

"That’s right," I said. "Well, I looked at that dime and that dollar and the choice was an easy one for me to make. I chose that shiny silver dollar and every year until they died fifteen years later I received birthday money from my auntys."
 

"You were sure smart to choose that silver dollar, aunty" said Danny.

"I’m not so sure about that," said Barney. "Aunty, may I borrow your calculator?

Why do you think Barney wanted to borrow my calculator? Do you think he suspected that I may have made a poor choice?
 

What do you think? Which would you have chosen? Can you give a good mathematical reason why your decision might be the best choice? Can you prove it?

When you think you know the answer, please post your solution on the message board. I will be waiting to hear from you and I will answer you if you tell me your strategy as well as your solution. Include your e-mail nickname or first name only, your teacher’s name and school, and your grade. Then check the web site in a few days for a personal message from me.

Love, Aunt Mathilda
( who is too old too soon – too wise too late!)