problem i'm having trouble with

[ak78]

A store currently charges the same price for each towe 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

© $3

(D) $4

(E) $12

 

I don't understand the phrase "10 fewer of the towels could be bought for $120" so this one completely threw me off. (Taken from PowerPrep CAT 2)

[riteshb]

I actually worked backwards using the answer choices instead of using an equation.

 

At $3, you can buy 40 towels right?

Now if the price is increased to $4, you can buy 30 towels now for $120.

[shaq]

Yes Ritesh's method is the shortcut.

 

The long method is ..

 

let number of towels bought for $120 = n

so price of a single towel = $ 120 / n

 

now price of 1 towel increases by $ 1

so new price of a single towel = $ (120 / n) + 1

no. of towel that could be bought at this price = n - 10

so new price of a single towel = $ 120 / (n -10)

 

so equating

 

so (120/n) + 1 = 120 / (n - 10)

(120 + n) / n = 120 / (n - 10)

n^2 -10n - 1200 = 0

(n-40)(n+30) = 0

n = 40 or n = -30

n= 40 = number of towels that could be bought at current price.

 

=> current price per towel = $ 120 / 40 = $ 3

 

so ans is C

[gmatguy]

ya

even i use the plugging in method ..

its 3

[thatchanon]

[clap] [clap] [clap] [clap] [clap] [clap]

[thatchanon]

Soory guy, I confused this question with another one in my test.