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?

Options:
Option 1: A chicken costs $6 and a duck costs $8
Option 2: A chicken costs $8 and a duck costs $6
Option 3: A chicken costs $10 and a duck costs $5
Option 4: A chicken costs $5 and a duck costs $10

Answer 1

By solving the system of linear equations derived from sales in two different months, it was determined that a chicken costs $8 and a duck costs $5. The correct option is B.

Step-by-step explanation:

The problem described is a system of linear equations which can be solved to determine the individual prices of chickens and ducks. The first equation represents the sales from last month: 50 chickens and 30 ducks for $550. The second equation represents this month's sales: 44 chickens and 36 ducks for $532. The system can be written as:

• 50c + 30d = 550
• 44c + 36d = 532

To find the solution, you can use the method of substitution or elimination. For instance, multiplying the first equation by 36 and the second equation by 30, to eliminate the variable d, will give:

• 1800c + 1080d = 19800
• 1320c + 1080d = 15960

Now, subtracting the second equation from the first gives:

480c = 3840

Dividing both sides by 480 yields:

c = $8

Now, substituting c = $8 back into one of the original equations to find the price of d gives:

50(8) + 30d = 550

400 + 30d = 550

30d = 550 - 400

30d = 150

d = $5

Therefore, a chicken costs $8 and a duck costs $5, which corresponds to Option 2 from the provided choices.