towels

Question

A store currently charges the same price for each towel that it sells. If the current price of each towel were increased $1, 10 fewer towels could be bought for $120. What is the current price of each towel?

$1
$2
$3
$4
$12

truplayer256 · Answer

Let's say that the store charges x dollars for each towel that it sells. When the store sells a total of y towels, it makes 120 dollars.

xy=120

We're told that if the price of each towel increase by $1, then 10 fewer towels could be bought for 120 dollars.

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

120-10x+y-10=120

y-10x=10

y=10(x)+10

(x)(10x+10)=120

x=3

sal2 · Answer

How do we know that xy=120? We only know that (x+1)(y-10)=120.

truplayer256 · Answer

How do we know that xy=120? We only know that (x+1)(y-10)=120.

"If the current price of each towel were increased $1, 10 fewer towels could be bought for $120.."

It is in this sentence that this problem specifies what xy must equal.

Baten80 · Answer

truplayer256 wrote:Let's say that the store charges x dollars for each towel that it sells. When the store sells a total of y towels, it makes 120 dollars.

xy=120

We're told that if the price of each towel increase by $1, then 10 fewer towels could be bought for 120 dollars.

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

120-10x+y-10=120

y-10x=10

y=10(x)+10

(x)(10x+10)=120

x=3

How do u solve the color part?

niksworth · Answer

Baten80 wrote:truplayer256 wrote:Let's say that the store charges x dollars for each towel that it sells. When the store sells a total of y towels, it makes 120 dollars. xy=120 We're told that if the price of each towel increase by $1, then 10 fewer towels could be bought for 120 dollars. (x+1)(y-10)=120 120-10x+y-10=120 y-10x=10 y=10(x)+10 (x)(10x+10)=120 x=3 How do u solve the color part? x(10x+10)=120 => 10x^2 + 10x = 120 => 10x^2 + 10x - 120 = 0 => 10(x^2 + x -12) = 0 => (x^2 + x - 12) = 0 => (x^2 + 4x - 3x - 12) = 0 => x(x+4) - 3(x+4) = 0 => (x+4)(x-3) = 0 => x = -4, 3 Since X can't be negative in the question, x = 3.

GMATGuruNY · Answer

Much easier to plug in the answers, which represent the current price of each towel. Let's try answer choice C, the middle value:

If each towel is $3:
For $120 we can buy 120/3 = 40 towels.
Increased price = 3+1 = $4 per towel.
120/4 = 30 towels.
40-30 = 10 fewer towels. Success!

Simple and sweet. The correct answer is C.

dayugsi · Answer

Two equations are needed here, I use "p" for the original towel price and "n" for the original number of towels.
EQ1: p*n=120 and EQ2: (p+1)*(n-10)=120
I found the wording tricky, when I first tried this problem, the challenge came from the "bought for $120" expression. I could not connect that $120 applied to EQ1 in enough time to finish the problem in 2 minutes...and even then, going the traditional algebraic way can take more than 2 minutes(for me at least). When I replaced "bought for" with "bought with"...then EQ1 came up in my head...the wording throws me off a bit...I think I need to get familiar with these "expressions" a bit more..
Anyhow, testing the values then allowed me to solve the problem within 2 minutes

EQ1: p*n=120 and EQ2: (p+1)*(n-10)=120
EQ1: 1*120=120 and EQ2: (1+1)*(120-10)=220 NOT A MATCH
EQ1: 2*60=120 and EQ2: (2+1)*(60-10)=150 NOT A MATCH
EQ1: 3*40=120 and EQ2: (3+1)*(40-10)=120 BINGO!!!

Rich.C@EMPOWERgmat.com · Answer

Hi dayugsi,

Most GMAT questions can be solved in a variety of ways, so you should look for alternatives to "math" approaches (in many cases, the math approach takes the longest to set up and complete).

Here, we're essentially asked to spend $120 on towels. We're then asked to figure out the price point at which ADDING $1 to the price of a towel results in 10 FEWER towels purchased. Since the answers are NUMBERS (and almost all consecutive integers), we can TEST THE ANSWERS....

IF....
Towels are....
$1 each, then we can buy 120 towels
$2 each, then we can buy 60 towels
$3 each, then we can buy 40 towels
$4 each, then we can buy 30 towels
$5 each, then we can buy 24 towels

Now, stop and look at the progression. We're looking for a point at which the DIFFERENCE is 10 towels. That only happens in one "spot" - when the price is increased from $3 to $4. The question asks for the current (re: lower) price.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Brent@GMATPrepNow · Answer

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

Here's an algebraic approach:

Let P = CURRENT price (in dollars)
So, P + 1 = NEW price (in dollars)

At P dollars apiece, the # of towels we can buy = 120/P
At (P+1) dollars apiece, the # of towels we can buy = 120/(P+1)
We're told we can buy 10 fewer towels at the NEW price.
So, (# of towels we can buy at CURRENT price) - (# of towels we can buy at NEW price) = 10
So, we can write: 120/P - 120/(P+1) = 10
SOLVE FOR P
Divide both sides by 10 to get: 12/P - 12/(P + 1) = 1
Multiply both sides by (P)(P+1) to get: 12(P+1) - 12P = P(P + 1)
Expand: 12P + 12 - 12P = P² + P
Rearrange: P² + P - 12 = 0
Factor: (P + 4)(P - 3) = 0
So, P = -4 or P = 3
P cannot be negative (since we can't have a negative price)
So, P must equal 3
Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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