Question

Michael breeds chickens and ducks. Last month, he sold 50 chickens and 30 ducks for $550 This month, he sold 44 chickens and 36 ducks for $532 How much does a chicken cost, and how much does a duck cost

Answer 1

A chicken cost $7.41

A duck cost $6.55

Step-by-step explanation:

Let x= price of chicken

And y= price of duck

Last month sales

50x + 30y= $550

This month sales

44x + 36y =$532

From last month sales

50x= $550-30y

x= $550-30y/50

Substitute x into this month sales

44($550-30y/50) - 36y =$532

Divide 44 and 50 by 2

22($550-30y/25) - 36y= $532

Open bracket

($12,100 - 660y)/25 - 36y = $532

Multiply

($12,100 - 660y) - 900y = $532

$12,100 - 660y -900y= $532

$12,100 - 1560y= $532

-1560y = $532 - $12,100

-1560y = $-11,568

Divide both sides by 1,560

y=$ -11,568/1,560

y=$ 7.41

Substitute the value of y into last month sales

50x + 30y = $550

50x + 30(7.4) = $550

50x + 222.6 = $550

50x = $550-222.6

50x=$327.4

Divide both sides by 50

x= $327.4/50

x=$6.55

Answer 2

each chicken costs $8 and each duck costs $5

Step-by-step explanation:

let C = chickens sold

let D = ducks sold

50C + 30D = 550

44C + 36D = 532 instead of replacing, we can multiply the second equation by -30/36 to be able to add both equations

50C + 30D = 550

-36.67C - 30D = -443.33

13.33C = 106.67

C = 106.67 / 13.33 = 8

30D = 550 - (50 x 8) = 550 - 400 = 150

D = 150 / 30 = 5