Eric is putting together alien toys called zerg and Borges for the display window in a toy store. He has a box of alien body parts that contains 45 heads and 55 feet. Each zerg must have one head and three feet.each Borg must have four heads and two feet. How many zergs and how many Borges can he make if he must use all the heads and feet in the box.

Question

Eric is putting together alien toys called zerg and Borges for the display window in a toy store. He has a box of alien body parts that contains 45 heads and 55 feet. Each zerg must have one head and three feet.each Borg must have four heads and two feet. How many zergs and how many Borges can he make if he must use all the heads and feet in the box.

Answer 1

Let the number of Zerg be z, and Borges be b.

Heads: 45 = z + 4b
Feet: 55 = 3z + 2b

Solve the simultaneous equations.

Hint: multiply the first by 3 and subtract the second, then simplify.

Hint 2: multiply the second by 3 and subtract the first, then simplify.

Answer 2

Let the number of Zerg be z, and Borges be b.

Heads: 45 = z + 4b
Feet: 55 = 3z + 2b

Solve the simultaneous equations.

Hint: multiply the first by 2 and subtract the second, then simplify.

Hint 2: multiply the second by 3 and subtract the first, then simplify.

Answer 3

To solve this problem, let's assume that Eric makes x number of zerg toys and y number of Borges.

Given that each zerg must have one head and three feet, and each Borg must have four heads and two feet, we can set up the following equations:

1x + 4y = 45 (equation for heads)
3x + 2y = 55 (equation for feet)

Now, we can solve this system of equations using the method of substitution or elimination.

Let's use the elimination method to solve this system:

Multiply the first equation by 3 and the second equation by 4 to eliminate the x term:

3(1x + 4y) = 3(45)
4(3x + 2y) = 4(55)

Simplifying these equations, we get:

3x + 12y = 135
12x + 8y = 220

Now, multiply the first equation by 4 and the second equation by 3 to eliminate the y term:

4(3x + 12y) = 4(135)
3(12x + 8y) = 3(220)

Simplifying these equations, we get:

12x + 48y = 540
36x + 24y = 660

Subtract the second equation from the first equation:

(12x + 48y) - (36x + 24y) = 540 - 660

Simplifying, we get:

-24x + 24y = -120

Divide through by -24:

x - y = 5

Now, we have a new equation:

x - y = 5 (equation 3)

To solve for x and y, we can use substitution.

Using equation 3, solve for x:

x = y + 5

Substitute this into equation 1:

1(y + 5) + 4y = 45

Simplifying, we get:

y + 5 + 4y = 45
5y + 5 = 45
5y = 40
y = 8

Substitute this value of y back into equation 3 to solve for x:

x - 8 = 5
x = 13

Therefore, Eric can make 13 zerg toys and 8 Borges using all the heads and feet in the box.