Answer:
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)
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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
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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
