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 aduck cost

Answer 1

Let C be the cost of the chicken, and D as the cost of the duck.

The equation is:

50c + 30d = 550 (divide this by 10)

5c + 3d = 55

3d = 55 - 5c (multiply by 3)

9d = 165 - 15c
Afterwards, 

44c + 36d = 532 (divide this by 4)

11c + 9d = 133

Substitute the value of 9d:

11c + 165 - 15c = 133

11c - 15c = 133 - 165

-4c = -32 (divide by -4)

c = 8

Therefore, the cost of each chicken is $8.00

Now going back to d,

9d = 165 - 15c (substitute c)

9d = 165 - 15(8)

9d = 165 - 120

9d = 45 (divide by 9)

d = 5
So the cost per duck is $5.00

Answer 2

Solution: Let the value of chickens be x and value of ducks be y. 50x + 30y = 550 -- equation 1 44x + 36y = 532 -- equation 2 Balancing the equation, multiplying the equation 1 with 44 and equation 2 with 50. 2200x + 1320y = 24200 --equation 3 2200x + 1800y = 26600 --equation 4 Subtract equation 4 from 3, -480y = -2400 y = 5 Putting value of y in equation 1, 50x + 30(5) = 550 50x + 150 = 550 x = 8 Cost of chicken = $8 Cost of duck = $5