Question

Abraham breeds chickens and ducks. Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532. How much does each chicken cost? How much does a duck cost?

Answer 1

Cost of one 🐣(chicken) = `color(orange)( $ 8`

Cost of one 🦆(duck) `color(indigo)( = $ 5`

Explanation:

Let c be 🐣 (chickens) and d be 🦆 (ducks)

Given : `50 🐣 + 30 🦆 = $ 550`

Dividing both sides by 10,

5 🐣 + 3 🦆 = 55 Eqn (1)

44 🐣 + 36 🦆 = $ 532

11 🐣 + 9 🦆 = 133 Eqn (2)

Multiply Eqn (1) by 3 to eliminate y term when subtraing Eqn (1) from (2).

Then a Eqn (1) becomes, 15 🐣 + 9 🦆 = 165 Eqn (3)

Subtracting Eqn (2) from (3),

(15 - 11) 🐣 = (165 - 133)

4 🐣 = 32 or 🐣 = $ 8.

Substituting value of 🐣 in Eqn (1),

(5 * 8) + 3 🦆 = 55

3 🦆 = 55 - 40 = 15

🦆 = 15 / 3 = $ 5