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A store currently charges the same price for each towel that [#permalink]
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27 Dec 2012, 05:47
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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
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Re: A store currently charges the same price for each towel that [#permalink]
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18 Oct 2013, 09:32
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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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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 \((p+1)(n10)=120\) 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 \(3n=120\) > \(n=40\) > \((3+1)(4010)=4*30=120\), 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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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 \((p+1)(n10)=120\) 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 \(3n=120\) > \(n=40\) > \((3+1)(4010)=4*30=120\), 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]
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17 May 2016, 04:50
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.
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Re: A store currently charges the same price for each towel that [#permalink]
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19 Oct 2013, 09:23
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]
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30 Oct 2013, 06:45
N = total no. of towel P = Price of towel
NP=120…(1), ; N = 120/p (N10)(P+1) = 120…(2)
From 2, NP+N10P10=120 120/P*P + 120/P 10P = 130 (Plugging from 1) 120/P 10P = 10 P^2+P12 = 0 (P+4)(P3)=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]
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20 Nov 2013, 05:29
(P+1)(N10)=NP N10P10=0 NP=120 => N=P/120 N10P10=0 P^2+P12=0 P=3
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Re: A store currently charges the same price for each towel that [#permalink]
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16 May 2014, 01:26
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 \((p+1)(n10)=120\) 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 \(3n=120\) > \(n=40\) > \((3+1)(4010)=4*30=120\), 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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Re: A store currently charges the same price for each towel that [#permalink]
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17 Sep 2014, 10:07
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 \((p+1)(n10)=120\) 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 \(3n=120\) > \(n=40\) > \((3+1)(4010)=4*30=120\), 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]
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17 Sep 2014, 11:22
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 \((p+1)(n10)=120\) 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 \(3n=120\) > \(n=40\) > \((3+1)(4010)=4*30=120\), 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, n10 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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Any idea of what's the level of this question?



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Re: A store currently charges the same price for each towel that [#permalink]
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16 Oct 2016, 19:19
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 original cost of towels = x \(\frac{120}{x} \frac{120}{(x+1)} = 10\) \(120 = 10(x^2 + x)\) (\(x^2 + x 12) = 0\) \((x+4)(x3)=0\) x=3
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