Question

How much does a chicken cost and duck?

Answer 1

Answer:

Chicken is $8

Duck is $5

Step-by-step explanation:

Step 1: Let $x$ represent the cost of chickens and let $y$ represent the cost ducks. Since we have two unknowns, we need two equations to find them.

Step 2: The total cost of chickens Michael sold last month can be shown as $50x$, and the total cost of ducks he sold last month can beshown as $30y$ Since these together add up to 550, we get these equations:

$50x+30y = 550$

We are also given that this month, Michael sold 44 chickens, and 36start text, 36 ducks, $532. This equaion can be expressed as:

$44x+36y=532$

Now that we have a system of the two equations, we can now go ahead and solve the two equations.

Step 3: We can now solve the system of equations by using the elimination method. Manipulate the equations so one of the variables has the same coefficients but with opposite signs.

$-6*50x+(-6)*30y\\=-300x-180y\\=-6*550\\=-3300$                  $5*44x+5*36y\\=220x+180y\\=5*532\\=2660$

Now eliminate $y$

$-300x-180y=-3300\\+220x+180y=2660\\=-80x-0=-640$

When we solve the resulting equation, we obtain that $x=8$. Then, we can substitute this into one of the original equations and solve for $y$ to obtain $y=5$.

Step 4: Recall that $x$ denotes the cost of a chicken and $y$ denotes the cost of a duck. Therefore, a chicken costs $8, and a duck costs $5