Question

A man buys 4 cows and 9 goats for $50,150. If he had purchased 9 cows and 4 goats, instead, then he would have to pay $40,750 more. What is the cost of one goat?

Answer 1

Answer:

one goat cost = $1350

Explanation:

let

 cow represent x

 Goat represent Y

4x + 9y = $50,150

9x + 4y = ($50,150 +$ 40750 = $91,900

4x + 9y = 50,150 ________(1)

9x + 4y = (50,150 + 40750) _______(2)

Add eqn 1 and eqn 2

13x + 13y = 141050

(divide both side by 13)

x + y = 10850 ________(3)

Subract eqn 1 and eqn 2

-5x + 5y = -40750

x - y = 8150 _________(4)

Make x subject of formula in eqn 4

x = 8150 + y

substitute  x = 8150 + y in eqn 3

8150 + y + y = 10850

8150 + 2y = 10850

2y = 10850 - 8150

2y = 2700

y = 1350

subtitute for y = 1350 in eqn  3

x + y = 10850

x = 10850 - y

x = 10850 - 1350

x = 9500

Cow cost $9500

Goat cost $1350