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A store currently charges the same price for each towel that

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A store currently charges the same price for each towel that [#permalink] New post 27 Dec 2012, 04:47
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A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
[Reveal] Spoiler: OA
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Re: A store currently charges the same price for each towel that [#permalink] New post 27 Dec 2012, 04:49
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Walkabout wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case $3. So, if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.
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Re: A store currently charges the same price for each towel that [#permalink] New post 18 Oct 2013, 08:32
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I thought it would be easier to just use a smart number.
I picked the middle number option (C) $3 per towel and proceeded to divide $120 with $3 to make 40 towels.
Then I tried with (D) $4 which gave me 30 towels.
Therefore the current price must be $3

Answer: C.
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Re: A store currently charges the same price for each towel that [#permalink] New post 15 May 2014, 09:27
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Bunuel wrote:
Walkabout wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case $3. So, if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.


Bunuel

Instead of two variables p,n cant it be solved in 1 variable as below

Say p = original price of 1 towel

so 120/p = 120/(p+1) + 10

putting values from options gives the value of p=3
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Re: A store currently charges the same price for each towel that [#permalink] New post 27 Aug 2013, 02:32
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Re: A store currently charges the same price for each towel that [#permalink] New post 19 Oct 2013, 08:23
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psychedelictwirl wrote:
I thought it would be easier to just use a smart number.
I picked the middle number option (C) $3 per towel and proceeded to divide $120 with $3 to make 40 towels.
Then I tried with (D) $4 which gave me 30 towels.
Therefore the current price must be $3

Answer: C.


I agree. I think this problem is a textbook example for why reverse plugging in is a valuable strategy.
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Re: A store currently charges the same price for each towel that [#permalink] New post 30 Oct 2013, 05:45
N = total no. of towel
P = Price of towel

NP=120…(1), ; N = 120/p
(N-10)(P+1) = 120…(2)

From 2,
NP+N-10P-10=120
120/P*P + 120/P -10P = 130 (Plugging from 1)
120/P -10P = 10
P^2+P-12 = 0
(P+4)(P-3)=0
Hence, P=3 (As price cannot be negative)

*This is indeed the long method, but I am comfortable with algebra, than plugging no.)
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Re: A store currently charges the same price for each towel that [#permalink] New post 20 Nov 2013, 04:29
(P+1)(N-10)=NP
N-10P-10=0

NP=120 => N=P/120
N-10P-10=0

P^2+P-12=0

P=3
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Re: A store currently charges the same price for each towel that [#permalink] New post 16 May 2014, 00:26
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himanshujovi wrote:
Bunuel wrote:
Walkabout wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case $3. So, if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.


Bunuel

Instead of two variables p,n cant it be solved in 1 variable as below

Say p = original price of 1 towel

so 120/p = 120/(p+1) + 10

putting values from options gives the value of p=3


Yes, that's correct.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A store currently charges the same price for each towel that [#permalink] New post 17 Sep 2014, 09:07
Bunuel wrote:
Walkabout wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case $3. So, if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.


Hi Bunnel

How is pn=120 first equation ??
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Re: A store currently charges the same price for each towel that [#permalink] New post 17 Sep 2014, 10:22
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SunthoshiTejaswi wrote:
Bunuel wrote:
Walkabout wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case $3. So, if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.


Hi Bunnel

How is pn=120 first equation ??


If the current price of each towel were to be increased by $1 (the current price p, new price p+1), 10 fewer of the towels (n for the current price, n-10 for new price) could be bought for $120.

So, for $120 for the current price p, we can buy n towels: pn=120.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A store currently charges the same price for each towel that   [#permalink] 17 Sep 2014, 10:22
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