Question

Michael 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 a chicken cost, and how much does a duck cost?

Answer 1

Let c = price of a chicken and d = price of a duck (in dollars). From the sales:

50c + 30d = 550 -> 5c + 3d = 55
44c + 36d = 532 -> 11c + 9d = 133

Multiply 5c + 3d = 55 by 3: 15c + 9d = 165. Subtract 11c + 9d = 133 to get 4c = 32, so c = 8. Then 5(8) + 3d = 55 gives 40 + 3d = 55, so d = 5.

A chicken costs $8 and a duck costs $5.