# For the last hour, you were watching birds at a feeder. You saw 6 cardinals, 9 chickadees, and 9 pigeons. In the next 2 hours, you saw a total of 36 birds. If the ratios of the number of each type of bird to the total number of birds were the same in these next two hours as they were in first hour, how many of each type of bird did you see? Explain your reasoning. The answer is 9 cardinals, 13.5 chickadees, and 13.5 pigeons. How?

In the first hour you see 6 cardinals, 9 chickadees, and 9 pigeons. In the next two hours you see 36 birds; the birds are in the same ratio as the first hour. How many of each type of bird did you see in the next two hours?

Since the number of birds by type is in the same ratio as the first hour, we know that the number of cardinals to the number of chickadees to the number of pigeons is 6x:9x:9x. Here x is an unknown variable.

Since we saw 36 birds we have 6x+9x+9x=36 which implies x=1.5.

Then the number of cardinals in the last two hours was 6(1.5)=9.
The number of chickadees in the last two hours was 9(1.5)=13.5.
The number of pigeons in the last two hours was 9(1.5)=13.5.

This is a perfectly good mathematical answer, but clearly it is impossible in the real world.