Andyis putting together alien toys called Zergs and Borgs for a display window in the toy shop. He has a box of body parts that contains 45 heads and 55 feet. One Zerg has 1 head and 3 feet. One Borg has 4 heads and 2 feet. How would I go about doing this?
Thank you in advance.
I don't need any answers I just need the equations. I could figure out the answers.
Anyone? Please help.
To figure out the number of Zergs and Borgs Andy can make using the given number of heads and feet, we can set up a system of equations.
Let's assume that Andy makes x Zergs and y Borgs.
One Zerg has 1 head, so x Zergs would require x heads.
One Zerg also has 3 feet, so x Zergs would require 3x feet.
Similarly, one Borg has 4 heads, so y Borgs would require 4y heads.
One Borg also has 2 feet, so y Borgs would require 2y feet.
We know that there are 45 heads and 55 feet available. We can set up the following equations based on that:
Equation 1: x heads + 4y heads = 45 (total number of heads)
Equation 2: 3x feet + 2y feet = 55 (total number of feet)
We can now solve this system of equations to find the values of x and y.
To do this, we can use a common method called substitution or elimination.
Let's solve the system of equations using the method of substitution.
From Equation 1, we can express y in terms of x:
y = (45 - x)/4
Substituting this value of y into Equation 2, we get:
3x + 2((45 - x)/4) = 55
Simplifying, we have:
3x + (90 - 2x)/4 = 55
Multiplying through by 4 to eliminate the fraction, we get:
12x + 90 - 2x = 220
Combining like terms, we have:
10x + 90 = 220
Subtracting 90 from both sides of the equation, we get:
10x = 130
Dividing both sides by 10, we find:
x = 13
Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:
13 heads + 4y heads = 45
4y = 32
y = 8
Therefore, Andy can make 13 Zergs and 8 Borgs using the given number of heads and feet.
Remember, these calculations are made under the assumption that Andy uses all available heads and feet in the box.