Çözüldü One-Variable Equations

If the length of each component of a wire after it was divided into twenty equal pieces was four centimeters shorter so that the wire could be cut into ten more equal pieces, how long is the wire?

A) 2.0
B) 2.1
C) 2.2
D) 2.3
E) 2.4

The initial length of each part before being divided first: x cm
Length of the wire: 20x cm....(I)
If each part were 4 cm shorter, their lengths would be x - 4 cm
In the second case, the length of the wire: (20 + 10)(x - 4) cm....(II)
Therefore, using the equations (I) and (II), 20x = 30(x - 4) ⇒ x = 12 cm
The length of the wire is 20·12 = 240 cm = 2.4 meters or from the equation (II) 30(12 - 4) / 100 = 2.4 meters.

Source: FDD (A Turkish Private Course Company) Publications