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A store currently charges the same price for each towel that [#permalink]
27 Dec 2012, 04:47

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

73% (02:58) correct
27% (02:22) wrong based on 590 sessions

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?

Re: A store currently charges the same price for each towel that [#permalink]
27 Dec 2012, 04:49

3

This post received KUDOS

Expert's post

5

This post was BOOKMARKED

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.

Re: A store currently charges the same price for each towel that [#permalink]
18 Oct 2013, 08:32

3

This post received KUDOS

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

Re: A store currently charges the same price for each towel that [#permalink]
19 Oct 2013, 08:23

Expert's post

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. _________________

Re: A store currently charges the same price for each towel that [#permalink]
15 May 2014, 09:27

3

This post received KUDOS

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

Re: A store currently charges the same price for each towel that [#permalink]
16 May 2014, 00:26

Expert's post

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

Re: A store currently charges the same price for each towel that [#permalink]
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.

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

Expert's post

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. _________________

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