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

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15 Jun 2006, 17:36

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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 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 current price be x
towels that can be bought with $120 = 120/x

If price is x+1, towels bought = 120/(x+1) = (120/x) - 10
Solving for x yields x=3

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 tax. What is the current price of each towel?

A) $1 B) $2 C) $3 D) $4 E) $12

Current price of each towel = $x

Number of current towels which can be bought for $120 is equal to (120/x)

amount of towels you could buy with old price is 120/x, and amount with new price is (120/x+1)-10

set these equations equal to each other, and solve for x. youll end up with a quadratic with roots -4 and 3. -4 is inadmissable, so 3 is your answer.

try it out: for 120 dollars, you can get 40 towels at 3 bucks a pop. Now, for a dollar increase, i.e. 4 dollars, you can get only 30 towels. Thats a difference of 10 towels due to a $1 increase in price.

Assuming n-no of towels, x-unit price of towel before increase:

n*x=120 (n-10)*(x+1)=120

You could solve the equations, but I tried different values of n ending with 0 from 120's prime factors - 5*3*2*2*2 so n could be 20, 30, 40 and corresponding x values are 6,4 and 3. And 40 and 3 satyisfy the second condition, so 3 is the answer.

OG 195. 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

Suggest shortest way to solve the problem.

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 C - $3 --> so if \(p=3\) then \(3n=120\) --> \(n=40\) --> \((3+1)(40-10)=4*30=120\), so this answer works.

A store currently charges the smae 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

I think there ought to be a comma between 1 and 10 here. If that were the case, we know that increasing price by 1 reduces volume by 10 for a fixed budget of 120. If initial price is x and volume y then we have

xy = 120

(x+1)*(y-10)=120

120 is 3*4*10

So, we can deduce that if x is 3 then y is 40 and when x+1 becomes 4, y-10 becomes 30 and hence x is 3 - Answer C