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

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

73% (02:57) correct
27% (02:17) wrong based on 453 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

3

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]
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]
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]
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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