A farmer asked his son: How many feet can I count when I am milking a cow? The boy replied: There are 6, 4 from the cow and 2 from you. The father then said: Actually, there are 9, because you forgot to count the 3 from the stool I sit on. Following this, the father proposed another problem to his son: In a corral, there are some people, cows, and stools, at least one of each. The total number of feet is 22 and the number of heads is 5. How many cows are there in the corral? The boy solved the problem correctly. What was his answer?
A) 1
B) 2
C) 3
D) 4
E) 5
Solution

## ALTERNATIVE C

The table below represents all possibilities for the number of heads to be 5 (we remember that stools do not have heads and there is at least one person and one cow).

| Heads |  | Feet | Feet of stools |
| :---: | :---: | :---: | :---: |
| Cows | People |  | (22 - feet, cows and people) |
| 1 | 4 | 12 | 10 |
| 2 | 3 | 14 | 8 |
| 3 | 2 | 16 | 6 |
| 4 | 1 | 18 | 4 |

The last column represents the possibilities for the number of feet of stools in the corral. Since each stool has 3 feet, the total number of feet of stools must be a multiple of 3. The
only multiple of 3 that appears in the last column is 6, corresponding to 2 stools. Therefore, in the corral there were 3 cows, 2 people, and 2 stools.