Two sorts
creatures
On Mars there are two sorts of creatures
Zerts have 4 legs and Zios have 7 legs.
Jacob the astronaut looked out of his space
ship and saw 55 legs.
• How many Zerts might there be ?
• How many Zios might there be?
•How many creatures might there be altogether?

There are two solutions:

There might be either 1 Zert and 12 Ziots or 5 Zerts and 5 Ziots.There might me either 13 or 10 creatures altogether.

Explanation:

This problem has a second question that is missing: Do you think there are any different answers?

You can create a system of two equations.

1. Name the variables:

x: number of of Zertsy: number of Zios

2. Translate the verbal statements into algebraic expressions:

Zerts have 4 legs: 4xZios have 7 legs: 7yJacob saw 55 legs: 4x + 7y = 55

3. Solution

Since there is one equation and two variables there could be many possible solutions, to the equation. But since x and y are restricted to positive integer numbers, the situation may be different.

You can test some numbers.

First, realize that the greatest possible value of y is when x = 0. Thus 7y has to be less than 55. The multiples of 7 that are less than 55 are 14, 21, 28, 35, 42, and 49.

Thus, the only possible values of y are 1, 2, 3, 4, 5, 6, and 7.

If y = 1: 4x = 55 - 7(1) = 48 ⇒ x = 48/4 = 12. Thus, this is your first solution: (12,5).

If y = 2: 4x = 55 -7(2) = 41. Since 41 is not muliple of 4. This is not a solution.

If y = 3: 4x = 55 - 21 = 34. 34 is not a multiple of 4. Not a solution.

If y = 4: 4x = 55 - 28 = 27. Not a solution, either.

If y = 5: 4x = 55 - 35 = 20 ⇒ x = 20/4 = 5. This is a second solution: (5,5)

If y = 6: 4x = 55 - 42 = 13. Not a multiple of 4.

If y = 7: 4x = 55 - 49 = 6. Not a multiple of 6.

Conclusion

There are two solutions:

There might be either 1 Zert and 12 Ziots or 5 Zerts and 5 Ziots.There might me either 13 or 10 creatures altogether.

Odysseus, against the wishes of his men, chooses to linger in the cave for some time until the dweller of the cave, Polyphemus, son of Poseidon, returns. Though he is initially courteous, he eventually commits his first horrible act by devouring two of Odysseus' men and imprisoning the rest for later consumption.

Explanation: