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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?

Respuesta :

nobillionaireNobley
Let the cost of a chicken be x and the cost of a duck, y, then

50x + 30y = 550 . . . (1)
44x + 36y = 532 . . . (2)

(1) x 6 ⇒ 300x + 180y = 3,300 . . . (3)
(2) x 5 ⇒ 220x + 180y = 2,660 . . . (4)

(3) - (4) ⇒ 80x = 640
⇒ x = 640 / 80 = 8

From (1): 50(8) + 30y = 550
⇒ 30y = 550 - 400 = 150
⇒ y = 150 / 30 = 5

Therefore, the price of a chicken is $8 and the price of a duck is $5.

The price of a single chicken is $8 and the price of a single duck is $5 and this can be determine by forming the linear equation in two variables.

Given :

  • Michael sold last month, 50 chickens and 30 ducks for $550.
  • This month, he sold 44 chickens and 36 ducks for $532.

Let the price of single chicken be 'a' and the price of single duck be 'b'. Then the linear equation will be:

[tex]50a + 30b = 550[/tex]  --- (1)

[tex]44a + 36b = 532[/tex]  --- (2)

Now, solve the equation (1) for 'b'.

[tex]b = \dfrac{550-50a}{30}[/tex]

[tex]b = \dfrac{55}{3}-\dfrac{5a}{3}[/tex]  ---- (3)

Now, put the value of 'b' in equation (2).

[tex]44a+36\left(\dfrac{55}{3}-\dfrac{5a}{3}\right) = 532[/tex]

[tex]44a+660-60a=532[/tex]

128 = 16a

a = 8

Now, put the value of a in equation (3).

[tex]b = \dfrac{55}{3}-\dfrac{5\times 8}{3}[/tex]

b = 5

The price of a single chicken is $8 and the price of a single duck is $5.

For more information, refer the link given below:

https://brainly.com/question/21835898

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