Bunuel wrote:
Tough and Tricky questions: Word Problems.
Jim went to the bakery to buy donuts for his office mates. He chose a quantity of similar donuts, for which he was charged a total of $15. As the donuts were being boxed, Jim noticed that a few of them were slightly ragged-looking so he complained to the clerk. The clerk immediately apologized and then gave Jim 3 extra donuts for free to make up for the damaged goods. As Jim left the shop, he realized that due to the addition of the 3 free donuts, the effective price of the donuts was reduced by $2 per dozen. How many donuts did Jim receive in the end?
(A) 18
(B) 21
(C) 24
(D) 28
(E) 33
Kudos for a correct solution.Given:
1. Jim went to the bakery to buy donuts for his office mates. He chose a quantity of similar donuts, for which he was charged a total of $15.
2. As the donuts were being boxed, Jim noticed that a few of them were slightly ragged-looking so he complained to the clerk. The clerk immediately apologized and then gave Jim 3 extra donuts for free to make up for the damaged goods.
3. As Jim left the shop, he realized that due to the addition of the 3 free donuts, the effective price of the donuts was reduced by $2 per dozen.
Asked: How many donuts did Jim receive in the end?
Let the price per donut be $x
Quantity of donuts purchased = 15/x
After receiving 3 extra donuts, Jim had = 15/x + 3 donuts
Effective price / donut reduced by = $2/dozen = $2/12 = $1/6
\(x - \frac{1}{6}= 15 / (\frac{15}{x} +3)\)
\((x - \frac{1}{6})(\frac{15}{x} + 3) = 15\)
\(15 - \frac{1}{6}* \frac{15}{x} +3x -\frac{1}{2} = 15\)
-2.5/x + 3x - .5 =0
6x - 5/x -1 =0
6x^2 -x -5=0
6x^2 - 6x + 5x -5 =0
(6x+1)(x-1)=0
x = 1
Quantity of donuts received in the end = 15/x +3 = 15 +3 = 18
IMO A
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