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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]

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New post 26 Mar 2018, 13:17
1
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.



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:)


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!
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A store currently charges the same price for each towel that  [#permalink]

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New post 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! :)
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A store currently charges the same price for each towel that  [#permalink]

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New post 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.

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

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New post 27 Mar 2018, 02:19
1
dave13 wrote:
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.

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!
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A store currently charges the same price for each towel that  [#permalink]

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

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New post 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

Answer: C.


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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New post 23 Jun 2019, 15:04
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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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