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# A store currently charges the same price for each towel that

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Senior PS Moderator
Joined: 26 Feb 2016
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A store currently charges the same price for each towel that  [#permalink]

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26 Mar 2018, 13:17
1
dave13 wrote:
Bunuel 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.

Hope it helps.

To whom it may concern

This is to testify that i dont i understand the following

here $$(p+1)(n-10)=120$$ where from do we get +1 and -10 ? whats the logic ?

we know that cost is insresed by 1.10 and another value we have is 120 ....

i sincerely dont understand the solution written by Zeus-Bunuel

Hi dave13

What we need to understand is if there are n towels being sold and the cost of a towel is p, n*p = 120$We are given this part in the question stem If the current price of each towel were to be increased by$1, 10 fewer of the towels could be bought for $120 Cost of towel goes up by 1 (p + 1) when there are 10 fewer towels bought (n-10) for the same$120
So basically the overall cost remains the same even though costs go up by $1 and the number of towels reduce by 10 Therefore, we write (p+1)*(n-10) = 120 Hope that helps you! _________________ You've got what it takes, but it will take everything you've got VP Joined: 09 Mar 2016 Posts: 1273 A store currently charges the same price for each towel that [#permalink] ### Show Tags 26 Mar 2018, 13:21 pushpitkc oh i misread the question i thought priced increased by 1.1 (by 1 dollar and 10 cents ) many thanks for clarification! VP Joined: 09 Mar 2016 Posts: 1273 A store currently charges the same price for each towel that [#permalink] ### Show Tags 26 Mar 2018, 13:49 JeffTargetTestPrep 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

Solution:

We can start by creating some variables.

Q = quantity of towels sold

P = price per towel sold

Next we can set up some equations.

We know that at the current price:

PQ = 120

We are next given that if the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for$120. From this we can say:

(P + 1)(Q – 10) = 120

Since we need to determine the value of P, we should get the second equation in terms of P only. We can do this by manipulating the equation PQ = 120. So we can say:

Q = 120/P

Now we can plug in 120/P for Q in the equation (P + 1)(Q – 10) = 120. We now have:

(P + 1)(120/P – 10) = 120

FOILing this, we get:

120 – 10P + 120/P – 10 = 120

–10P + 120/P – 10 = 0

We can multiply the entire equation by P to get rid of the denominators. This gives us:

–10P^2 + 120 – 10P = 0

10P^2 + 10P – 120 = 0

P^2 + P – 12 = 0

(P + 4)(P – 3) = 0

P = -4 or P = 3

Since P can’t be negative, P = 3.

JeffTargetTestPrep hello hope my question finds you well

what rule did you use that you changed places of values and its signs ?

from this –10P^2 + 120 – 10P = 0

to this 10P^2 + 10P – 120 = 0

pushpitkc any idea how ?
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Joined: 26 Feb 2016
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Location: India
GPA: 3.12
Re: A store currently charges the same price for each towel that  [#permalink]

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27 Mar 2018, 02:19
1
dave13 wrote:
JeffTargetTestPrep 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 Solution: We can start by creating some variables. Q = quantity of towels sold P = price per towel sold Next we can set up some equations. We know that at the current price: PQ = 120 We are next given that if the current price of each towel were to be increased by$1, 10 fewer of the towels could be bought for $120. From this we can say: (P + 1)(Q – 10) = 120 Since we need to determine the value of P, we should get the second equation in terms of P only. We can do this by manipulating the equation PQ = 120. So we can say: Q = 120/P Now we can plug in 120/P for Q in the equation (P + 1)(Q – 10) = 120. We now have: (P + 1)(120/P – 10) = 120 FOILing this, we get: 120 – 10P + 120/P – 10 = 120 –10P + 120/P – 10 = 0 We can multiply the entire equation by P to get rid of the denominators. This gives us: –10P^2 + 120 – 10P = 0 10P^2 + 10P – 120 = 0 P^2 + P – 12 = 0 (P + 4)(P – 3) = 0 P = -4 or P = 3 Since P can’t be negative, P = 3. Answer is C. JeffTargetTestPrep hello hope my question finds you well what rule did you use that you changed places of values and its signs ? from this –10P^2 + 120 – 10P = 0 to this 10P^2 + 10P – 120 = 0 pushpitkc any idea how ? Hey dave13 This equation $$-10P^2 + 120 – 10P = 0$$ is nothing but -($$10P^2 + 10P - 120$$ = 0) When we multiply both the sides by -1, we get $$10P^2 + 10P - 120 = 0$$ Hope this helps you! _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 3094 A store currently charges the same price for each towel that [#permalink] ### Show Tags 27 Mar 2018, 10:15 dave13 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. @dave13 wrote:To whom it may concern This is to testify that i dont i understand the following here $$(p+1)(n-10)=120$$ where from do we get +1 and -10 ? whats the logic ? we know that cost is insresed by 1.10 and another value we have is 120 .... i sincerely dont understand the solution written by Zeus-Bunuel please help:) dave13 , you wanna testify, do you? Better not let me get you on cross-ex. I'll do direct examination instead. In this Wonderland court I can lead my own witness and I can testify. Bunuel is NOT working directly with a percent increase multiplier. How about (my witness!) we strike that from the record. He does not have to work with a multiplier, because we have an actual dollar value increase AND the actual decrease in the # of towels. +1 means = +$1 per towel
-10 means = we can buy 10 fewer towels than we could at the lower price

The logic? We have an original equation and a new equation.
The new equation expresses the increase in price (+$1) and the decrease in quantity (-10) The original equation: p = price of each towel n = number of towels p*n = Total Price (Ex.: p=$2, n=10. Ten towels at $2 ea = p*n =$20)

--Price goes UP by $1? That's just (p +$1)
--# of towels at that price DECREASES by 10? That's (n-10) towels

If price per towel goes up, you can buy fewer towels than the original # of towels, because RHS total price stays the same.

You can only spend $120. Originally, p*n = 120 Then price changes. Now you have increased price per towel (p +$1)
And we are GIVEN the decreased # of towels: (n-10 towels)

p * n = $120 (Original) (p + 1)(n - 10) =$120 (New)
Don't solve the equations

Put the answer choices into them.
--For the answer choice, use (p*n) to find original # of towels
--Then use second equation with increased price to find new # of towels

Use ONLY (p) and (p+1). Solve for # of towels, n

Let's try D) $4 = current price How many towels can we buy at$4 ea?
p * n = $120$4 * n = $120 n = 30 towels Price goes UP by$1.
Now each towel costs $(p+1)=($4+1)= $5 How many can we buy for$5 each?
$5 * n =$120
n = 24 towels

Before we could buy 30. Now we can buy 24. That's SIX fewer towels. Not 10 fewer. WRONG.

Try C) $3 is current price How many towels can we buy at$3 each?
$3 * n =$120
n = 40 towels

Price increases by $1.$(p+1) =$(3+1)=$4
How many towels can we buy at $4 each?$4 * n = $120 n = 30 Before, we could buy 40. Price increased. Now we can buy only 30. How many fewer towels at higher price? (40-30)= 10 fewer towels Bingo. Answer C Does that help? _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. -- Take another look. Take a look around. These are the moments you can't pass by. Intern Joined: 08 Dec 2018 Posts: 14 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 23 Jun 2019, 08:12 WillEconomistGMAT wrote: 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

I agree. I think this problem is a textbook example for why reverse plugging in is a valuable strategy.

Can you please explain the question by this strategy.
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Re: A store currently charges the same price for each towel that  [#permalink]

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23 Jun 2019, 15:04
1
Hi AmanMatta,

This question can certainly be solved by TESTing THE ANSWERS (a Tactic in which you 'plug in' answers to see if they "fit" the given information; even when an answer doesn't fit, you can often determine whether that answer is 'too big' or 'too small' and narrow down the remaining possibilities).

Here, we're told that a certain number of towels can be bought for $120 and that increasing the price of a towel by$1 will decrease the total number of towels purchased by 10. We're asked for the CURRENT price of a towel. Let's start by TESTing Answer B:

Answer B: $2 If the current price is$2, then we can buy $120/$2 = 60 towels
Increasing the price to $3 means that we could then buy$120/$3 = 40 towels That's a decrease of 20 towels, which is NOT a match (it's supposed to be 10 towels). We need the difference to be SMALLER, so we need fewer towels at each step. Let's raise the price.... Answer D:$4

If the current price is $4, then we can buy$120/$4 = 30 towels Increasing the price to$5 means that we could then buy $120/$5 = 24 towels
That's a decrease of 6 towels, which is NOT a match (it's supposed to be 10 towels). We need the difference to be BIGGER, so we need more towels at each step - and we should lower the price. There's only one answer left that makes sense...

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Re: A store currently charges the same price for each towel that   [#permalink] 23 Jun 2019, 15:04

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