2. Due to the price reduction of $20 \%$, for 240 denars, one can buy 1 meter more fabric than what could be bought for 270 denars before the reduction. Determine the price of the fabric before the reduction.
Solution. Let $x$ be the number of meters purchased at a price of $y$ denars per meter for 270 denars. Then from the condition of the problem, we have $x y=270, (x+1) \frac{80 y}{100}=240$, from which we get $x=9$ and $y=30$.