trnguyen wrote:A store currently charges the same price for each towel that it sells. If the current prie 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.

Thank you in advance for your help.

120/X vs 120/(x+1)

N towel vs N-10 towels

just looking at these two statements

120/3 vs 120/4

40 vs 30

so it is $ 3

if you ask for math :

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

1 / x(x+1) = 1/12

so x(x+1)=12 you can either leave it here and see 3x4 = 12

or

X^2+x-12=0

(x+4)(x-3)=0

X=-4 it can't be
X=3 BINGO!

Problems like this also work great with guessing numbers. If you're fast with your mental math, there's no reason you can't solve this problem in under a minute without using equations.

The one concrete number we have is $120. So, I'd pick some number that works nicely with 120 to try it out. Let's say we pick 60 towels at $2 each. If we raise the price $1, we'd have 50 towels at $3 each. Those numbers don't work, since BOTH sets need to add up to $120.

Let's take 40 towels at $3 each. If we raise the price $1, we have 30 towels at $4 each. Since both those sets add up to $120, those are the right numbers.

Hope this helps!