A flying saucer filled with space aliens landed in my front yard! After the entire crew had filed 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 creatures landed in my yard?
Green creatures_____________
Blue creatures______________
Please do not keep reposting the same question. Give us at least a couple of hours for a tutor to respond.
Ok subtracting leaders heads means 88 heads for green and blue.
Subtracting leaders feet, that leaves 120 feet for green and blue.
B*4+G*2=120
G+B=88/2
now solve for G, B
24 of blue and green
12 green, 32 blue because 12 x 2 = 24 and 32 x 3 = 96 and 24 + 96 = 120
also 12 = 32 = 44
you don't count the heads and the legs you run for dear life
Remember, my face cool, and yours is not!!!!!!!!!!!!
To find out how many of each type of creature landed in your yard, we can use a system of equations.
Let's assign variables to the number of each type of creature:
- Let's call the number of purple creatures P.
- Let's call the number of green creatures G.
- Let's call the number of blue creatures B.
Based on the given information, we know the following:
1) P + (G + B) = 91 (total number of heads)
2) 4P + (2G + 3B) = 124 (total number of feet)
Now, let's solve these equations simultaneously.
From equation 1, we can rewrite it as:
P = 91 - (G + B)
Substituting this into equation 2:
4(91 - (G + B)) + 2G + 3B = 124
Expanding and simplifying the equation:
364 - 4G - 4B + 2G + 3B = 124
364 - 2G - B = 124
-2G - B = 124 - 364
-2G - B = -240
Now, we can solve for one variable in terms of the other:
B = -2G + 240
Next, we'll substitute this expression for B into equation 1:
P + G + (-2G + 240) = 91
P - G = 91 - 240
P - G = -149
At this point, we can eliminate P by adding equation P - G = -149 to equation B = -2G + 240:
(P - G) + (-2G - B) = -149 + (-240)
P - 3G - B = -389
Since we know that the purple creature has three heads and four feet, we can substitute P = 3 and B = 4 into the equation:
3 - 3G - 4 = -389
-4 - 3G = -389
-3G = -389 + 4
-3G = -385
G = -385 / -3
G = 385 / 3
G = 128.33 (rounding down to the nearest whole number)
Since you can't have a fraction of a creature, we can conclude that there are 128 green creatures in your yard.
Now, we can substitute the value of G back into the equation B = -2G + 240:
B = -2(128) + 240
B = -256 + 240
B = -16
Again, since you can't have a negative number of creatures, we know that there are 16 blue creatures in your yard.
Finally, we can find the number of purple creatures by substituting the values of G and B into the equation P - G = -149:
P - 128 = -149
P = -149 + 128
P = -21
Once again, since you can't have a negative number of creatures, in this case, it means that there are no purple creatures in your yard.
To summarize:
Green creatures: 128
Blue creatures: 16