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Molly went to a gift shop to buy some Christmas cards. Due to insuffic

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Molly went to a gift shop to buy some Christmas cards. Due to insuffic  [#permalink]

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New post 28 Feb 2019, 07:47
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Difficulty:

  35% (medium)

Question Stats:

76% (02:57) correct 24% (03:29) wrong based on 33 sessions

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Molly went to a gift shop to buy some Christmas cards. Due to insufficient money at that time, she decided to come back on the next day. The next day price per card was increased by $4 and she could buy 12 fewer cards than those she would have bought on the previous day for $135. What is the new price of each card? (Note: All the cards are equally priced).

A. 4
B. 5
C. 6
D. 9
E. 11
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Re: Molly went to a gift shop to buy some Christmas cards. Due to insuffic  [#permalink]

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New post 28 Feb 2019, 20:46
1
kiran120680 wrote:
Molly went to a gift shop to buy some Christmas cards. Due to insufficient money at that time, she decided to come back on the next day. The next day price per card was increased by $4 and she could buy 12 fewer cards than those she would have bought on the previous day for $135. What is the new price of each card? (Note: All the cards are equally priced).

A. 4
B. 5
C. 6
D. 9
E. 11



Various ways to do it..

(I) Use the choices..
A. 4... New price is 4, old price is 0... Not possible
B. 5... New price 5, old price 5-4=1.. Difference in cards = \(\frac{135}{1}-\frac{135}{5}=135-27\neq{12}\)
C. 6.. New price 6, old price 6-4=2.. Difference in cards = \(\frac{135}{2}-\frac{135}{6}\neq{12}\)
D. 9.. New price 9, old price 9-4=5.. Difference in cards = \(\frac{135}{5}-\frac{135}{9}=27-15=12\) YES
E. 11.. New price 11, old price 11-4=7.. Difference in cards = \(\frac{135}{7}-\frac{135}{11}\neq{12}\) Answer cannot be in fractions

(II) Algebraic
New price x and old price x-4..
\(\frac{135}{x-4}-\frac{135}{x}=135*\frac{x-x+4}{x(x-4)}=12.....135*4=12x^2-48x....x^2-4x-45=0.....(x-9)(x+5)=0\)
Hence x can be 9 or -5. Cannot be negative, so x=9

D
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Re: Molly went to a gift shop to buy some Christmas cards. Due to insuffic  [#permalink]

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New post 03 Mar 2019, 03:59
1
let price of card be x $
so with 135$ , Molly could buy ; 135/x = y cards --(1)

now with 4$ increase she can buy y-12 cards
or say
135/x+4= y-12-(2)
solve 1 & 2
we ger
12x^2+48x-540=0
or say
x=-9, +5
x cannot be -ve
so initial price 5$ , new price ; 5+4 = 9 $
IMO D

kiran120680 wrote:
Molly went to a gift shop to buy some Christmas cards. Due to insufficient money at that time, she decided to come back on the next day. The next day price per card was increased by $4 and she could buy 12 fewer cards than those she would have bought on the previous day for $135. What is the new price of each card? (Note: All the cards are equally priced).

A. 4
B. 5
C. 6
D. 9
E. 11

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Re: Molly went to a gift shop to buy some Christmas cards. Due to insuffic   [#permalink] 03 Mar 2019, 03:59
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