Problem A and Solution

Banana Bonanza

Three monkeys found a tree that has \(54\) bananas growing on it. Each monkey eats two bananas a day from the tree, and no other animals eat any of the bananas.

How many bananas will be left on the tree at the end of the first day?

If they start eating from the tree on a Monday, on what day of the week will they eat the last banana?

Since each monkey eats \(2\) bananas and there are \(3\) monkeys, this means \(2 + 2 + 2\) or \(2 \times 3 = 6\) bananas are eaten from the tree each day. Since the tree started with \(54\) bananas, this means it will have \(54 - 6 = 48\) bananas left at the end of the first day.

We can make a table to keep track of how many bananas are left on the tree at the end of each day, knowing that the monkeys eat \(6\) bananas a day. From part (a), we know that there are \(48\) bananas left at the end of the first Monday.

**Day****Bananas Left at End of Day**Monday \(48\) Tuesday \(42\) Wednesday \(36\) Thursday \(30\) Friday \(24\) Saturday \(18\) Sunday \(12\) Monday \(6\) Tuesday \(0\)

From this table, we can see that they will eat the last banana on a Tuesday.