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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.

Respuesta :

absor201

The cost of one chicken is $8 and cost of one duck is $5.

Step-by-step explanation:

Let,

Cost of one chicken = x

Cost of one duck = y

According to given statement;

50x+30y=550    Eqn 1

44x+36y=532     Eqn 2

Multiplying Eqn 1 by 36

[tex]36(50x+30y=550)\\1800x+1080y=19800\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 30

[tex]30(44x+36y=532)\\1320x+1080y=15960\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](1800x+1080y)-(1320x+1080y)=19800-15960\\1800x+1080y-1320x-1080y=3840\\480x=3840[/tex]

Dividing both sides by 480

[tex]\frac{480x}{480}=\frac{3840}{480}\\x=8[/tex]

Putting x=8 in Eqn 1;

[tex]50(8)+30y=550\\400+30y=550\\30y=550-400\\30y=150[/tex]

Dividing both sides by 30

[tex]\frac{30y}{30}=\frac{150}{30}\\y=5[/tex]

The cost of one chicken is $8 and cost of one duck is $5.

Keywords: linear equation, elimination method

Learn more about linear equations at:

  • brainly.com/question/10987396
  • brainly.com/question/10989800

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