Question from Rodger, a teacher:

How Many Oranges?

Marjorie, Colleen, and Bob picked oranges together. They were tired after picking a large number of oranges and so fell asleep. Marjorie woke first and decided to take her third of the oranges and head home. She counted the oranges, and found that the number was divisible by 3 if she took one of the oranges first. Marjorie took one orange and then took one-third of the remaining oranges. She left quietly.

Bob awoke a short time later, noticed that Colleen was sleeping, and presumed Marjorie had gone for a walk. He decided to head home because he wasn't feeling well. Not realizing that anyone had left, he counted the oranges and found that the number of oranges was two more than a number that could be easily divided by 3. So he took the two extra oranges and then one-third of what was left. He left without waking Colleen and without waiting for Marjorie to return.

Colleen finally awoke and wondered where her friends had gone. She assumed they were both busy somewhere nearby. Before she left, she counted the oranges and was surprised at how small the number was. She found that the number of oranges was one more than a multiple of three, so she took the extra orange and one third of those remaining.

1. What was the total number of oranges the friends picked?

2. How many oranges were left behind when Colleen departed?

3. Is more than one answer possible for the total number of oranges? If so, what other numbers are possible? Explain.

4. Based on the values you found in problem 3, determine a reasonable solution to the problem. Explain your answer.

5. Is it possible that five oranges remained after Colleen took her share? Explain.

6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain

7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern

5. Is it possible that five oranges remained after Colleen took her “share”? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern