Linear equations

Question

A rod WZ is cut into 3 parts, WX, XY, and YZ respectively. If WY:YZ=2:1, WX:XZ=2:3, and XY=8 cm, find the length of the rod.

Answer 1

Set a=WX; b=XY=8; and c=YZ

Since WY = WX + XY, we know that (a + 8) is to 2, as c is to 1

2       a + 8
--- = ------
1         c


So, 2c = a + 8, which means that c = 0.5a + 4



Since XZ = XY + YZ = 8 + (0.5a + 4), we know that a is to 2 as (0.5a + 12) is to 3


2              a
--- = ---------------
3        (0.5a + 12)

which means that 3a = a + 24

So, 2a = 24, and a = 12


So, WX = a = 12; XY = 8; and YZ = c = 0.5(12) + 4 = 10

 

Answer 2

Removed due to arithmetic error. See Paul H.'s solution. Mark M.