SOLUTION: A man bought some chickens for ₦60. If he had obtained 5 more for the same money, they would have cost ₦2 less each. How chickens did he buy?

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Question 1134406: A man bought some chickens for ₦60. If he had obtained 5 more for the same money, they would have cost ₦2 less each. How chickens did he buy?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "n" be the number of chickens he bought (the value under the question).


Then the price for one chicken is  60%2Fn.


Had he bought (n+5) chickens for the same money, the price for one chicken in this hypothetical case would be  60%2F%28n%2B5%29.


From the condition,


    60%2Fn - 60%2F%28n%2B5%29 = 2.


It is your basic equation to solve.


    Looking into the equation, you can guess its solution mentally and momentarily:  n = 10.


To solve it algebraically, multiply both sides by n*(n+5). You will get


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

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

    2n^2 + 10n - 300 = 0

    n^2 + 5n - 150 = 0

    (n-10)*(n+15)) = 0.


Of two roots  n= 10  and  n= -15, only positive  n= 10 is meaningful.


Answer.  n= 10 chickens.

Solved.

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Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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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