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?
a chicken costs $ and a duck costs $.
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Explanation:

Step1: Define variables

Let $c$ = cost of a chicken, $d$ = cost of a duck.

Step2: Set up equations

$$50c + 30d = 550$$
$$44c + 36d = 532$$

Step3: Simplify first equation

Divide by 10: $5c + 3d = 55$ → $3d = 55 - 5c$

Step4: Simplify second equation

Divide by 4: $11c + 9d = 133$

Step5: Substitute $3d$ into second equation

Substitute $3d = 55 - 5c$ → $11c + 3(55 - 5c) = 133$
Expand: $11c + 165 - 15c = 133$
Simplify: $-4c = 133 - 165 = -32$
Solve for $c$: $c = \frac{-32}{-4} = 8$

Step6: Solve for $d$

Substitute $c=8$ into $3d = 55 - 5c$:
$3d = 55 - 5(8) = 55 - 40 = 15$
$d = \frac{15}{3} = 5$

Answer:

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