Question

2. The Martian Zoological Society has a unique display of the native monocephalous fauna:

Tripods (three feet each) and Pentapods (five feet each). When I was there, I counted 20 heads
and 84 feet.
a.) Draw a picture to find the solution.
b.) Set up a system of equations to make sure your "picture" answer is correct. Show your
work.

Answer 1

There are 12 pentapods and 8 Tripods, which in total add up to 84 feet.

Explanation:

Given that both the Tripods and the Pentapods have, at least, 3 feet (the Pentapods have 5), and that in total between both groups they add 20 heads and 84 feet, the following logical reasoning can be made:

If there are 20 heads, there are 20 Martians in all. Each of them has, at least, 3 feet, with which in principle the 20 Martians would add up to a total of 60 feet (20 x 3). Therefore, there is a surplus of 24 feet (84 - 60).

If the Pentapods have 2 feet more than the Tripods, the number of Pentapods in the total Martians is determined by that difference. Thus, if there are 24 feet left, there are 12 Pentapods (24/2).

Therefore, in the group of Martians there are 12 pentapods (12 x 5 = 60) and 8 Tripods (8 x 3 = 24), which in total add up to 84 feet (60 + 24).