Allysa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana

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 Americana chickens, A,

and the number of Delaware chickens, D, she purchased.

Determine algebraically how many of each type of chicken Allysa purchased.

8 Delaware chickens and 4 Americana chickens

Answer: Allysa purchased 4 Americana chickens and 8 Delaware chickens✔️

Step-by-step explanation:

From the information they provide us, we have to establish the necessary equations to solve the problem.

Let A be the American chickens and D be the Delaware chickens.

Allysa purchased 12 chickens:

A + D = 12 } Equation 1

Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Allysa spent $35:

$3.75A + $2.50D = $35 } Equation 2

We take the value of A from equation 1 and substitute it into equation 2:

A = 12 - D } Equation 1

$3.75A + $2.50D = $35 } Equation 2

$3.75 (12 - D) + $2.50D = $35

$3.75·12 - $3.75D + $2.50D = $35

$45 - $3.75D + $2.50D = $35

$45 - $35 = $3.75D - $2.50D

$10 = $1.25D

D = $10/$1.25 = 8, Delaware chickens

A = 12 - D = 12 - 8 = 4, Americana chickens

Answer: Allysa purchased 4 Americana chickens and 8 Delaware chickens✔️

Check

We can substitute these values in the equation 2

$3.75A + $2.50D = $35 } Equation 2

$3.75·4 + $2.50·8 = $15 + $20 = $35 ✔️Checked!

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