Answer: She would have $23.34 at the end of first week
Step-by-step explanation
The total number of chickens = 12
Let A represent the Americana chicken
Let D represent the delware chicken
Since, there are total of 12 chickens
Therefore, the algebraic expression can be represented mathematically as follows
A + D = 12 ------------------ equation 1
Each Americana chicken is sold for $3.75
Each Delware chicken is sold for $2.50
The total 12 chickens is purchased at $35
3.75 x A + 2.50 x D = 35
3.75A + 2.5D = 35 --------------- equation 2
The two equations can be solved simultaneously using substitution method
A + D = 12
3.75A + 2.5D = 35
Make A the subject of the formula in equation 1
A = 12 - D
Put A = 12 -D in equation 2
3.75(12 - D) + 2.5D = 35
Open the parenthesis
45 - 3.75D + 2.5D = 35
Collect the like terms
-3.75D + 2.5D = 35 - 45
-1.25D = -10
Divide both sides by -1.25
-1.25D/-1.25 = -10/-1.25
D = 10/1.25
D = 8 chickens
To find A, put the value of D in equation 1
A + D = 12
A + 8 = 12
A = 12 - 8
A = 4 chickens
Therefore, we have 8 Delware chickens and 4 Americana chickens
Part B
Determine how much money she expects to take at the end of first week
The americana chicken lay 2 eggs per day
Since, we have 4 americana chickens
Each chicken lays 2 eggs
4 x 2 = 8 eggs
The 4 chickens lay 8 eggs in one day
7 days = 1 week
in one week, they would laid 8 x 7
= 56 eggs
Therefore, Americana chickens would laid 56 eggs in one week
The Delware chicken lay 1 egg per day
We have a total of 8 Delware chickens
Total eggs laid in a day = 8 x 1
= 8 eggs
In one week = 8 x 7
= 56 eggs
Therefore, Delaware chickens would also laid 56 eggs in one week
The total number of eggs laid in one week = 56 + 56
Total eggs = 112 eggs
She do sell per dozen for $2.50
1 dozen = 12 eggs
The total eggs laid = 9 dozens 4 eggs
9 dozens of eggs = 9 x 2.50
9 dozens = $22.50
If 12 eggs is sold at $2.50
Then 1 egg will be sold at what
12 = 2.50
1 = x
cross multiply
x * 12 = 2.50 * 1
12x = 2.50
Divide both sides by 12
12x/12 = 2.50/12
x = 2.50/12
x = $0.21
Therefore one egg is sold for $0.21
For the remaining 4 eggs
0.21 x 4 = $0.84
Total money she will be expecting is = 22.50 + 0.84
= $23.34
Therefore, she would have $23.34 at the end of first week