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At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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15 Jun 2017, 23:41
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At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 00:01
Bunuel wrote: At a party, John collected $96 to buy p equallypriced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?
A. $6 B. $8 C. $9 D. $10 E. $12 Let price per pizza be \(x.\) Total number of pizza \(= p\) Price of \(x\) pizza's before discount \(= $96\) \(px = 96\)  (i) Total number of pizza after discount \(= p + 4\) Price decrease on each pizza after discount \(= x  2\) Given Price of pizza's after discount is \($96\). ie; \((p+4)(x2) = 96\) \(px + 4x 2p  8 = 96\) \(96 + 4x  2p 8 = 96\)  (Substituting value of \(px\) from (i)) \(4x  2p  8 = 0\) \(4x  2p = 8\) \(2x  p = 4\) \(p = 2x + 4\)  (ii) Substituting value of \(p\) from (ii) in equation (i), we get; \((2x+ 4)x = 96\) \(2x^2 + 4x = 96\) \(2x^2  4x  96 = 0\) \(x^2  2x  48 = 0\) \(x^2  8x + 6x  48 = 0\) \(x(x  8) + 6 (x  8) = 0\) \((x+6)(x+8) = 0\) \(x = 8, 6\) Price cannot be negative. Therefore price of each pizza before discount was \($8\). Price of pizza after discount is \(82 = $6.\) Answer (A).



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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 00:14
Bunuel wrote: At a party, John collected $96 to buy p equallypriced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?
A. $6 B. $8 C. $9 D. $10 E. $12 Let the price for each pizza be x. Thus, \(p*x = 96\) {no. of pizza*price of each pizza = Total sum of money John had} =>\(p = \frac{96}{x}\)  eqn. (1) After the discount, reduced price of each pizza = \((x2)\) and thus, he could buy 4 extra pizza. So, no. of pizzas becomes \((p+4)\) thus the equation changes to : (p+4)*(x2) = 96 =>\(p+4 = \frac{96}{(x2)}\)  eqn (2) Equating eqn. 1 and 2 \(\frac{96}{(x2)} = \frac{96}{x} + 4\) =>\(\frac{96}{(x2)}  \frac{96}{x} = 4\) Taking LCM and solving results in \(4x(x2) = 192\) => \(4x^2  8x = 192\) => \(x^2 2x  48 = 0\) => \((x8)(x+6) = 0\) => \(x = 8 or 6\). As the price cant be a negative value, \(x= 8\) As x was the original price for the pizzas, i.e., price before discount, price after discount = \((x2)\) = \(6\) Option A.



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At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 02:22
Since John bought p equally priced pizzas, with 96$, and we assume each of the pizza cost 'c' From the question stem pc = 96 96(when prime factorized) gives \(2^5*3\) The cost of the pizza's cannot be \(9(3^2)\) and \(10(2*5)\). So Option C and D are out! The second part of the question, gives us the price during promotion (p + 4)(c  2) = 96 Now evaluating the answer options, Since price of pizza (after discount) is 8$, John would have bought 12 pizza's during the promotional period. However, price before discount would be 10$ and he would have bought 8 pizza's which doesn't give us 96$ as total cost. Hence, Option C is also not right If price after discount is 6$, he would have bought 16 pizza's during the promotional period. However, price before discount would be 8$ and he would have bought 12 pizza's which gives us 96$ as total revenue. Hence, Option A is our answer
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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 03:23
Bunuel wrote: At a party, John collected $96 to buy p equallypriced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?
A. $6 B. $8 C. $9 D. $10 E. $12 Instead of taking variables and solving the equations, this question can be best done by jumping to the options directly. John collected $96 to buy p pizzas, each of same price. So obviously, 96 will be divisible by p, and by the undiscounted price of the pizza. The discounted price is $2 less and bought 4 more pizzas i.e. p + 4 pizzas. The discounted price would be divisible by 96 too. Looking at the options, 6 and 8 could be the discounted and undiscounted prices. At $6, you would get 96/6 = 16 pizzas At $8, you would get 96/8 = 12 pizzas (4 less) (A match) Hence discounted price is $6 Answer (A)
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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 04:12
We can do 'plugin answers' as well. If total no. of pizzas is p, then price per pizza is 96/p. Price after discount is 96/p2. Plug in for 10: 96/p2 = 10, => p = 8. Now, originally price per pizza was 96/8 = 12 (rs2 off) but 96/10 = 9.6 (not four extra pizzas). So we look at a lesser no. Plugin for 6, 96/p2 = 6, => p = 12. Now price per pizza = 96/12 = 8. (rs 2 off) and 96/6 = 16, which is 4 extra pizzas. Ans is A



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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 04:37
VeritasPrepKarishma wrote: Bunuel wrote: At a party, John collected $96 to buy p equallypriced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?
A. $6 B. $8 C. $9 D. $10 E. $12 Instead of taking variables and solving the equations, this question can be best done by jumping to the options directly. John collected $96 to buy p pizzas, each of same price. So obviously, 96 will be divisible by p, and by the undiscounted price of the pizza. The discounted price is $2 less and bought 4 more pizzas i.e. p + 4 pizzas. The discounted price would be divisible by 96 too. Looking at the options, 6 and 8 could be the discounted and undiscounted prices. At $6, you would get 96/6 = 16 pizzas At $8, you would get 96/8 = 12 pizzas (4 less) (A match) Hence discounted price is $6 Answer (A) That's how I went about it, however my concern was assuming that the $96 had to be divisible by both p and p+4 (especially the latter). They wouldn't have to say that there was any $ left over after in either case, right?



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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 12:53
96/p = cost before discount after discount: 96/p  2
thus: (96/p 2)*(p+4) = 96
p = 12, price after discount: $6 Answer OA



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Re: At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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16 Jun 2017, 20:45
Excellent Question Bunuel. Here is what I did on this one > Cost 1 = Cost 2 96 => (96/p  2 ) (p+4) Solving this we get => p=12 or p=16 Hence p=12 So the cost after the discount would be 96/12  2 => 82 => 6 Hence A Great Question
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At a party, John collected $96 to buy p equallypriced pizzas. When [#permalink]
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17 Sep 2017, 02:04
Price after discount as per options given are: 6, 8, 9, 10, 12 Price before discount: 8,10,11,12,14 Price after discount and before discount should divide 96. Combination of 6 and 8 does it, therefore answer is A




At a party, John collected $96 to buy p equallypriced pizzas. When
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