Question

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

Answer 1

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