13.248. There are two identical pieces of fabric. The cost of the entire first piece is 126 rubles more than the cost of the second. The cost of four meters of fabric from the first piece exceeds the cost of three meters of fabric from the second piece by 135 rubles. A customer bought 3 meters of fabric from the first piece and 4 meters of fabric from the second piece and paid 382 rubles 50 kopecks for everything. How many meters of fabric were in each of these pieces? What is the cost of one meter of fabric from each piece?
Solution.

Let $x$ rubles be the cost of the second piece, $x+126$ - the cost of the first, $y$ m - the length of one piece.

Then the cost of 1 m of the first fabric is $\frac{x+126}{y}$ rubles, 1 m of the second is $-\frac{x}{y}$ rubles.

By the condition $\left\{\begin{array}{l}4 \frac{x+126}{y}-3 \frac{x}{y}=135, \\ 3 \frac{x+126}{y}+4 \frac{x}{y}=382.5,\end{array}\right.$
from which $\left\{\begin{array}{l}\frac{x+126}{y}=67.5, \\ \frac{x}{y}=45,\end{array}\right.$ and, therefore, $y=5.6$ m.

Answer: 5.6 m; 67 rubles 50 kopecks and 45 rubles.