Three Pieces of Fabric Length Problem

Understanding the Problem

We have three pieces of fabric with original lengths:

• First piece: $x$ meters



• Second piece: $y$ meters



• Third piece: $z$ meters

Their combined length is 120 meters:

$x + y + z = 120$

Fractions cut from each piece:

1. First piece: $\frac{3}{5}$ cut → remaining: $\frac{2}{5}x$



2. Second piece: $\frac{2}{3}$ cut → remaining: $\frac{1}{3}y$



3. Third piece: $\frac{1}{2}$ cut → remaining: $\frac{1}{2}z$

After cutting, remaining lengths are equal:

$\frac{2}{5}x = \frac{1}{3}y = \frac{1}{2}z$

Setting Up Equations

Let equal remaining length be $k$:

1. $\frac{2}{5}x = k$ → $x = \frac{5}{2}k$



2. $\frac{1}{3}y = k$ → $y = 3k$



3. $\frac{1}{2}z = k$ → $z = 2k$

Substitute into total length equation: