Respuesta :
Answer:
The cost of each chicken were $3 and each duck were $13.33.
Step-by-step explanation:
Given:
In one month I sold 50 chickens and 30 ducks for $550.
The next month I sold 44 chickens and 30 ducks for $532.
Now, to find the number of chickens and ducks.
Let the cost of a chicken be [tex]x.[/tex]
And the cost of a duck be [tex]y.[/tex]
So, in 1 month I sold 50 chickens and 30 ducks for $550.
[tex]50x+30y=550[/tex] .........(1)
Now, in the next month I sold 44 chickens and 30 ducks for $532.
[tex]44x+30y=532[/tex] ........(2)
So, to get the number of chickens and ducks we solve by elimination method:
[tex]50x+30y=550[/tex]
[tex]44x+30y=532[/tex]
Subtracting both the equations:
[tex]50x+30y-(44x+30y)=550-532[/tex]
[tex]50x+30y-44x-30y=550-532[/tex]
[tex]6x=18[/tex]
Dividing both sides by 6 we get:
[tex]x=3.[/tex]
The cost of a chicken = $3.
Now, putting the value of [tex]x[/tex] in equation (1):
[tex]50x+30y=550\\50(3)+30y=550\\150+30y=550[/tex]
Subtracting both sides by 150 we get:
[tex]30y=400[/tex]
Dividing both sides by 30 we get:
[tex]y=13.33[/tex].
The cost of a duck = $13.33.
Therefore, the cost of each chicken were $3 and each duck were $13.33.
