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? Please Help ASAP

a chicken cost $4

a duck cost $11.66

Step-by-step explanation:

Let the cost of one chicken be x

then cost of 50 chicken = 50x

cost of one duck be y

cost of 30 ducks = 30y

It is given that  50 chickens and 30 ducks cost $550

thus

50x+30y = 550

dividing LHS and RHS by 10 we have

50x/10+30y/10 = 550/10

=>5x+3y = 55 (1)

for this month we have calculation as given below

cost of 44 chicken = 44x

cost of 36 ducks = 36y

It is given that  44 chickens and 36 ducks cost $532

thus

44x+36y = 532

dividing LHS and RHS by 4 we have

44x/4+36y/4 = 532/4

=>11x+9y = 133  2

we have equation

5x+3y = 55 (1)

11x+9y = 133  2

multiplying equation 1 by 3 on LHS and RHS we have.

(note: multiplication with3 is done to transform 3y into 9y

so that y can be removed from equation)

5x*3+3y*3 = 55*3

=> 15x+9y = 165  ___(3)

subtracting equation 3 from equation 1 we have

15x+9y = 165

-(11x+9y )= 133

15x +9y -11x -9y = 165 - 133

=> 4x = 32

=> x = 32/4 = 4

5x+3y = 55

=>5*4 +3y = 55

=>20+ 3y = 55

=>3y = 55-20 = 35

=>y = 35/3 =11.66

Thus,a chicken cost $4

a duck cost $11.66

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step-by-step explanation: vsfdvsfvd