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.

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?

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"