Question

Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532. How much does a chicken cost, and how much does a duck cost?

Answer 1

Let the cost of a chicken be x and the cost of a duck, y, then

50x + 30y = 550 . . . (1)
44x + 36y = 532 . . . (2)

(1) x 6 ⇒ 300x + 180y = 3,300 . . . (3)
(2) x 5 ⇒ 220x + 180y = 2,660 . . . (4)

(3) - (4) ⇒ 80x = 640
⇒ x = 640 / 80 = 8

From (1): 50(8) + 30y = 550
⇒ 30y = 550 - 400 = 150
⇒ y = 150 / 30 = 5

Therefore, the price of a chicken is $8 and the price of a duck is $5.