A farmer has chickens, sheep and horses there are 154 animals and 516 total legs the number of sheep equals twice the number of
chickens how many of each type of animals does he have
1 answer:
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
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