you get 2 equations:

pn = 120 or n = 120/p
(p+1)(n-10) = 120 or (p+1)(120/p-10)=120

solving for p:

(p+1)(120/p-10)=120
(p+1)(12/p-1)=12
(12-p)+(12/p-1)=12
12p-p^2+12-p=12p
p^2+p-12=0
(p+4)(p-3)=0

p= -4 or 3 since we can't have negative towels the answer is 3

I think for this particular problem the best strategy is to look at the answers provided and see that 3 is the best choice. $120 buys you 40 towels at $3 each and 30 (10 less) at 4$ (+1) each.

the algebra is the easier part the harder part. THe harder part of this is the english to algebraic translation. How to do that is puzzling me!?

Enginpasa1 wrote:the algebra is the easier part the harder part. THe harder part of this is the english to algebraic translation. How to do that is puzzling me!?

Hi Enginpasa1, like xilef said, I think that this problem is meant to puzzle you while you try to resolve two equations . The best and most effefctive way IMO to solve this question is by using the answer choices and seeing what fits.

you start with 12$ a shirt for example, see how many you can buy for 120$ (that's 10) and how many you can buy for one dollar more, or 13$ (that's less than 10) incorrect answer. move on to 4$ a shirt, you can buy 30 shirts for 120$, and 22 shirts for 5$, we're looking for a difference of 10 shirts so [D] isn't it either. try [C] and see that it fits.

Try working this way instead of building complicated equations.

still confused which one is the correct answer