Question 1134406
x = number of chickens.
y = price for each chicken.


your two equation that need to be solved simultaneously are:


x * y = 60
(x+5) * (y-2) = 60

in the first equation, you buy x chickens at a price of y each for a total expenditure of 60 nigerian naira.


in the second equation, you buy x + 5 chickens at a price of y - 2 each for a total expenditure of 60 nigerian naira.


in the first equation, solve for y to get y = 60/x.


in the second equation, replace y with 60/x to get:


(x+5)*(y-2) = 60 becomes (x+5)*(60/x-2) = 60


multiply both sides of this equation by x to get:


(x+5)*(60-2x) = 60x


simplify this to get:


60x-2x^2+300-10x = 60x


subtract 60x from both sides of this equation to get:


-2x^2+300-10x = 0


divide both sides of this equation by 2 to get:


-x^2+150-5x = 0


multiply both sides of this equation by -1 and arrange the terms in descending order of degree to get:


x^2+5x-150 = 0


factor this quadratic equation to get x = 10 or x = -15.


x can't be negative, so it has to be 10.


when x = 10, x*y=60 becomes 10*y=60 which gets you y = 6


you have x = 10 and y = 6


(x+5)*(y-2) becomes 15*4=60


looks like the solution is good.


he can buy 10 chickens at 6 each for a total of 60 nigerian naira or he can buy 15 chickens at 4 each for a total of 60 nigerian naira.


you could also have solved this graphically.


you would graph both equations of x*y=60 and (x+5)*(y-2)=60


the intersection of the two graphs that gives you a positive value for x and y is your solution.


that solution tells you that x = 10 and y = 6.


the graph is shown below.


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