Allysa spent $35 to purchase 12 chickens. She bought two different types of chickens. American chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of American chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Extension: Each American chicken lays 2 eggs per day and sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.

Let’s define the variables: A = number of American chickens D = number of Delaware chickens Write the system of equations based on the problem Total chickens: A + D = 12 Total cost: 3.75A + 2.50D = 35 Solve the system algebraically Step 1: From the first equation: D = 12 - A Step 2: Substitute into the second: 3.75A + 2.50(12 - A) = 35 Step 3: Distribute: 3.75A + 30 - 2.50A = 35 Step 4: Combine like terms: 1.25A + 30 = 35 Step 5: Subtract 30 from both sides: 1.25A = 5 Step 6: Divide both sides by 1.25: A = 5/1.25 = 4 Step 7: Now, find D: D = 12 - A = 12 - 4 = 8 Allysa purchased: 4 American chickens 8 Delaware chickens Extension: Calculating the expected revenue Each American chicken lays 2 eggs per day, so: 2 * 7 = 14 eggs per week per American chicken Total eggs from all American chickens: 14 * 4 = 56 eggs Total eggs from Delaware chickens (assuming they also lay 2 eggs per day): 14 * 8 = 112 eggs (if they lay the same amount) But based on the information, only the American chickens’ eggs are considered for revenue. Total eggs from American chickens: 14 * 4 = 56 eggs Number of full dozens: 56/12 = 4.66 dozens Revenue: 4.66 * 2.50 = 11.65 Assuming only American chickens’ eggs are sold, Allysa will earn approximately $11.65 at the end of the week.