A flying saucer filled with space aliens landed in my front yard!After the entire crew had filled out of their spaceship, I happened to count their heads and feet. I saw a total of 91 heads and 124 feet. It was clear that their leader was a purple creature with three heads and four feet. The rest of the space aliens each had two heads. The green ones had two feet and the blue ones had three feet. How many of each type of creature landed in my yard?
______GREEN ONES ______BLUE ONES
h = heads = 91
f = feet = 124
3 + 2g + 2b = 91
4 + 2g + 3b = 124
2g + 2b = 88
2g + 3b = 120
b = 32
g = 12
Call 911!
I think the green creatures had about 12 and for the amount of blue creatures is 32 and the exception of the leader of the aliens which states that it had 3 heads and 4 feet to complete the solution of this problem.
To solve this problem, let's assign variables to represent each type of creature.
Let's say:
- x = the number of purple creatures
- y = the number of green creatures
- z = the number of blue creatures
We know that the leader, who is purple, has 3 heads and 4 feet. So, there is only 1 purple creature, which means x = 1.
The rest of the creatures, which are not purple, each have 2 heads. Therefore, the number of green and blue creatures combined is 91 - 3 (the head count of the purple creature), which is 88.
Now let's consider the number of feet. The green creatures have 2 feet each, and the blue creatures have 3 feet each. So, the total number of feet is 2y + 3z.
We know that the total number of feet is 124, so we can set up an equation:
2y + 3z = 124
Now let's solve the system of equations:
From x = 1, we know there is one purple creature.
From the equation 2y + 3z = 124, we know the number of green and blue creatures combined is 88.
To find the number of each, we can make assumptions and test them with the information given. Let's start by assuming there are 44 green creatures and 44 blue creatures:
2(44) + 3(44) = 88 + 132 = 220
This assumption does not give us the total number of feet (124).
Let's try another assumption:
Assume there are 43 green creatures and 45 blue creatures:
2(43) + 3(45) = 86 + 135 = 221
This assumption also does not give us the total number of feet (124).
We have narrowed it down to possibilities where there are fewer blue creatures. Let's continue testing assumptions to find the exact numbers of green and blue creatures.
Assuming 42 green creatures:
2(42) + 3z = 124
84 + 3z = 124
3z = 40
z = 40/3 (not a whole number)
Assuming 41 green creatures:
2(41) + 3z = 124
82 + 3z = 124
3z = 42
z = 42/3 (not a whole number)
Finally, assuming 40 green creatures:
2(40) + 3z = 124
80 + 3z = 124
3z = 44
z = 44/3 (not a whole number)
Based on the assumptions we have tested, it seems that there might be a mistake or inconsistency in the information given. There doesn't appear to be a whole number solution for the number of green and blue creatures. It's possible that there is an error in the problem statement or some information is missing.
Without a whole number solution, we cannot determine the exact number of green and blue creatures.