Question

Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532. How much does a chicken cost, and how much does a duck cost? A chicken costs \$$dollar sign and a duck costs \$$dollar sign .

Answer 1

Answer:

A chicken costs $8 and a Duck costs $5.

Step-by-step explanation:

Let the cost of each chickens be 'x'.

Also Let the cost of each ducks be 'y'.

Now given:

Data of Last month:

Number of chickens sold = 50

Number of ducks sold = 30

Total money made = $550

Now we can say that;

Total money made is equal to sum of Number of chickens sold multiplied by cost of each chickens and Number of ducks sold multiplied by cost of each ducks

framing in equation form we get;

$50x+30y =550$

Now dividing both side by 10 we get;

$\frac{50x}{10}+\frac{30y}{10}=\frac{550}{10}\\\\5x+3y=55 \ \ \ \ equation \ 1$

Now This month Data:

Number of chickens sold = 44

Number of ducks sold = 36

Total money made = $532

Now we can say that;

Total money made is equal to sum of Number of chickens sold multiplied by cost of each chickens and Number of ducks sold multiplied by cost of each ducks

framing in equation form we get;

$44x+36y =532$

Now dividing both side by 4 we get;

$\frac{44x}{4}+\frac{36y}{4}=\frac{532}{4}\\\\11x+9y=133 \ \ \ \ equation \ 2$

Now multiplying equation 1 by 3 we get;

$3(5x+3y)=55\times3\\\\15x+9y=165 \ \ \ \ equation \ 3$

Subtracting equation 2 from equation 3 we get;

$15x+9y-(11x+9y)=165-133\\\\15x+9y-11x-9y= 32\\\\4x=32$

Dividing both side by 4 we get;

$\frac{4x}{4}=\frac{32}{4}\\\\x=\ 8$

Now Substituting the value of x in equation 1 we get;

$5x+3y=55\\\\5\times8+3y =55\\\\40+3y=55\\\\3y =55-40\\\\3y =15\\\\y = \frac{15}{3} =\ 5$

Hence A chicken costs $8 and a Duck costs $5.