Question

A paddock contains ducks and sheep. There are a total of 42 heads and 96 feet in the paddock. Determine how many ducks and how many sheep are in the paddock using simultaneous elimination.

Answer 1

Answer:

Number of ducks in paddock = 36

Number of sheep in paddock = 6

Step-by-step explanation:

Let d be the number of ducks and s be the number of sheep

Then according to given statements, the equations will be:

$d+s = 42\ \ \ Eqn\ 1\\2d+4s = 96\ \ \ Eqn\ 2$

For elimination, multiplying equation 1 by 2 and then subtracting from equation 2:

$2(d+s) = 2*42\\2d+2s = 84\\Subtraction:\\2d+4s-(2d+2s) = 96-84\\2d+4s-2d-2s = 12\\2s = 12\\\frac{2s}{2} = \frac{12}{2}\\s = 6$

Putting s = 6 in equation 1:

$d+6 = 42\\d = 42-6\\d = 36$

Hence,

Number of ducks in paddock = 36

Number of sheep in paddock = 6

Answer 2

Number of sheep and Number of duck are 6 and 36

Elimination method:

Given that;

Number of total heads = 42

Number of total feet = 96

Find:

Number of ducks and sheep

Computation:

Number of legs in 1 sheep = 4

Number of legs in 1 duck = 2

So,

Assume;

Number of sheep = a

Number of duck = b

So,

a + b = 42 ...... Eq1

4a + 2b = 96 ......... Eq2

Eq2 / 2

2a + b = 48..... Eq3

From Eq 3 and Eq1

a = 6

So,

b = 36

Number of sheep = 6

Number of duck = 36

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