Answer:
number of chicken = 50
number of sheep = 100
number of horse = 4
Step-by-step explanation:
Let
x = number of chicken
y = number of sheep
z = number of horse
x + y + z = 154 (1)
2x + 4y + 4z = 516 (2)
the number of sheep equals twice the number of chickens
y = 2x
Substitute into the equation
x + y + z = 154
x + 2x + z = 154
3x + z = 154 (3)
2x + 4y + 4z = 516
2x + 4(2x) + 4z = 516
2x + 8x + 4z = 516
10x + 4z = 516 (4)
3x + z = 154 (3)
10x + 4z = 516 (4)
Multiply (3) by 4 to eliminate z
12x + 4z = 616 (5)
10x + 4z = 516 (4)
Subtract (4) from (5)
12x - 10x = 616 - 516
2x = 100
x = 100/2
x = 50
Recall,
y = 2x
y = 2(50)
y = 100
x + y + z = 154
50 + 100 + z = 154
150 + z = 154
z = 154 - 150
z = 4
number of chicken = 50
number of sheep = 100
number of horse = 4
