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Answer:
The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
Step-by-step explanation:
Given:
Let the number of Americana chickens be 'x'.
Let the number of Delaware chickens be 'y'.
Number of chickens purchased = 12
Now we know that;
Number of chickens purchased is equal to sum of the number of Americana chickens and the number of Delaware chickens.
framing in equation form we get;
[tex]x+y =12 \ \ \ \ equation\ 1[/tex]
Also Given:
Cost of Americana chickens = $3.75
Cost of Delaware chickens = $2.50
Total amount spent = $35
Now we know that;
Total amount spent is equal to sum of the number of Americana chickens multiplied by Cost of Americana chickens and the number of Delaware chickens multiplied Cost of Delaware chickens.
framing in equation form we get;
[tex]3.75x+2.5y =35 \ \ \ \ equation\ 2[/tex]
Hence The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Now to find the number of each type of chickens she purchased we will solve the above equation.
First we will multiply equation 1 with 2.5 we get;
[tex]2.5(x+y)=12\times2.5\\\\2.5x.+2.5y = 30 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]3.75x+2.5y-(2.5x+2.5y)=35-30\\\\3.75x+2.5y-2.5x-2.5y=5\\\\1.25x=5[/tex]
Now Dividing both side by 1.25 we get;
[tex]\frac{1.25x}{1.25}=\frac{5}{1.25}\\\\x= 4[/tex]
Now we will substitute the value of 'x' in equation 1 we get;
[tex]x+y=12\\\\4+y=12\\\\y=12-4 = 8[/tex]
Hence Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Now Given:
Number of eggs laid by American chicken per day = 2 eggs
Number of eggs laid by Delaware chicken per day = 1 egg
Cost of 12 eggs = $2.5
Total number of days = 7
Now first we will find the Total number of eggs laid by both the chickens.
Total number of eggs laid per day = [tex]4\times2 + 8\times 1= 8 +8 =16\ eggs[/tex]
Total number of eggs laid in week = [tex]16\times7= 112[/tex] eggs
12 eggs = $2.5
112 eggs = Cost of 112 eggs.
By cross multiplication we get;
Cost of 112 eggs = [tex]\frac{2.5 \times 112}{12} = \$23.33[/tex]
Hence Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
The system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased are as follows;
A + D = 12
3.75A + 2.50D = 35
Alyssa purchased 4 Americans chicken and 8 Delaware chickens.
She is expected to take in $22.5 at the end of the first week with her 12 chickens.
number of Americana chickens = A
number of Delaware chickens = D
Therefore,
A + D = 12
3.75A + 2.50D = 35
A = 12 - D
3.75(12 - D) + 2.50D = 35
45 - 3.75D + 2.50D = 35
-1.25D = -10
D = -10 / -1.25
D = 8
A = 12 - 8 = 4
A = 4
Therefore, Alyssa bought 4 Americans chickens and 8 Delaware chickens.
Each American chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day.
She only sells the egg in full dozen for $2.50.
The amount of money she expects to take in at the end of the first week with her 12 chickens is calculated as follows.
1 week = 7 days
Number of American chicken eggs(first week) = 7 × 4 × 2 = 56 eggs
Number of Delaware chicken eggs(first week) = 1 × 7 × 8 = 56 eggs
Total eggs = 56 + 56 = 112 eggs.
She can only sell full dozen of eggs. Therefore,
112 / 12 = 9.333
1 dozen = $2.50
9 dozen =
cross multiply
Amount made from the eggs = 9 × 2.50 = $22.5
learn more about system of equation: https://brainly.com/question/15319423?referrer=searchResults
