Question 1104681: A fruit seller was selling imported bananas. I told him to give me Rs. 120 worth of bananas. After he gave me the bananas, I told him that they were too small, and forced him to give me 2 extra bananas for free. He complained that because of giving me these two extra bananas, he is getting Rs. 10 per dozen less on this transaction than the original price. How many bananas did I get (including the 2 extra bananas)?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of bananas he bought.
let y equal the price for each banana.
you get x bananas for y price per banana for a total of 120.
your formula becomes x * y = 120.
x is the number of bananas.
y is the price per banana.
when you get 2 bananas for free, the price the vendor gets is 10 less per dozen.
10 less per dozen is equal to 10/12 less per banana.
your new formula is (x+2) * (y - 10/12) = 120
x + 2 is the number of bananas he gets.
y - 10/12 is the price per banana.
put y - 10/12 under a common denominator and you get 12y/12 - 10/12 which is equal to (12y - 10)/12 price per banana.
the new formula becomes (x+2) * (12y-10)/12 = 120.
from x * y = 120, solve for x to get x = 120 / y
replace x with 120/y and the new formula becomes (120/y + 2) * (12y - 10)/12 = 120.
multiply both sides of the equation by y to get y * (120/y + 2) * (12y - 10)/12 = 120 * y
multiply both sides of the equation by 12 to get y * (120/y + 2) * 12 * (12y - 10) / 12 = 120 * y * 12
y * (120/y + 2) becomes (120 + 2y)
12 * (12y - 10) / 12 becomes (12y - 10)
120 * y * 12 becomes 1440 * y
formula becomes (120 + 2y) * (12y - 10) = 1440 * y
distribute the multiplication on the left side of the equation to get 1440y - 1200 + 24y^2 - 20y = 1440y
the 1440y on the left and right side of the equation cancel out and you are left with -1200 + 24y^2 - 20y = 0
reorder the terms in descending order of degree to get 24y^2 - 20y - 1200 = 0
solve this quadratic equation to get y = 7.5 or y = -6.6666666666667
y can't be negative, so you get y = 7.5.
that's the price per banana that the vendor would have normally gotten.
in the equation of x * y = 120, replace y with 7.5 to get x * 7.5 = 120.
solve for x to get x = 120 / 7.5 = 16.
you originally were going to buy 16 bananas.
you insisted on getting 2 free bananas, so the vendor gave you 18 bananas instead of 16.
the fruit vendor complained that, by giving you the 2 free bananas, his price per dozen bananas was reduced by 10.
you bought 16 bananas for 120 at a price of 7.5 per banana.
when you got 18 bananas for the same 120, then the price per banana dropped from 7.5 per banana to (6 + 2/3) per banana.
his price per dozen would have been 7.5 * 12 = 90.
his price per dozen dropped to (6 + 2/3) * 12 = 80.
the vendor's price per dozen dropped by 10, as he complained that it did.
you were asked to determine how many bananas you got including the extra two.
the answer to that is 18.
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