Gina and Tom raise cat and birds. They counted all of their animals' heads and got a sum of 10. They counted all of their feet and got a sum of 34.
Question 1: How many cats and birds do they have?
Question 2: Does your answer change if you do not assume that they have to have at least one animal of each type?
Question 3: If you knew that they also had at least one snake, would your answer to the first question change?
Hint: Draw a picture to represent the problem situation, letting the letter X represent each cat and the letter I represent each bird...and think about why the letters X and I are being used.
Solution Commentary: This oldie has been investigated by students even at the elementary school level, and it will not be spoiled here by provision of "the" solution here.
Part of the fascination allowed a teacher is to watch as students choose problem solving processes to implement...pictures, equations, graphs, etc. When one sees a student using determinants and/or Gaussian elimination to solve this problem, one should be reminded of the adage: Once you have a hammer, everything looks like nails.
Also, I should add that the inclusion of a snake was suggested by my own seventh grade students more than 30 years ago.