Costs of Goats and Sheep At the Brendan Berger ranch 6 goats

Costs of Goats and Sheep At the Brendan Berger ranch, 6 goats and 5 sheep sell for $305, while 2 goats and 9 sheep sell for $285. Find the cost of a single goat and of a single sheep.

Solution

Given that

Cost of 6 goats and 5 sheep = $305

Cost of 2 goats and 9 sheep = $285

Let goats denoted by G and sheep denoted by S

Hence,

6G + 5S = $305.............................1

2G + 9S = $285.............................2

Solve equations 1 and 2

Multiply equation 2 with 3

   2G + 9S = $285

6G + 27S = $855

6G = $855 - 27S........................................3

From equation 1

   6G + 5S = $305

6G = $305 - 5S...................................................4

Equating the equations 3 and 4

  6G = $855 - 27S

6G = $305 - 5S

Hence,

  $855 - 27S = $305 - 5S

$855 - $305 = -5S + 27S

$550 = 22S

22S = $550

S = $550/22

S = $25

Substitute S = $25 in equation 2

2G + 9S = $285

2G + 9 ( $25) = $285

2G = $285 - $225

2G = $60

G = $60/2

G = $30

Hence,

Cost of each goat = $30

Cost of each sheep = $25