Question

How much does a chicken cost and duck?

Answer 1

Chicken is $8

Duck is $5

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