A plumber had two pipes. The ratioof the length of the longer pipe to the shorter pipe was 9 : 2 when he cut 1.65 meter from the longer pipe the remaining lengt

x = the longer pipe
y = the shorter pipe
x : y = 9 : 2
2x = 9y
x = 9y/2

x - 1,65 = 3y
x = 3y + 1,65

x1 = x2
9y/2 = 3y + 1,65
9y = 2(3y + 1,65)
9y = 6y + 3,3
9y-6y = 3,3
3y = 3,3
y = 3,3/3 = 1,1 m

So the shorter pipe is 1,1 meter

let
x be the length of the longer pipe and
y be the length of the shorter pipe

the given ratio means
[tex] \frac{x}{y} = \frac{9}{2} [/tex]
so,
[tex]x = \frac{9}{2} y[/tex]

when he cut 1.65 meter from the longer pipe the remaining length was 3 times that of the shorter pipe, it means
[tex]x - 1.65 = 3y \\ x = 3y + 1.65[/tex]

substitute x
[tex]x = x \\ \frac{9}{2} y = 3y + 1.65 [/tex]

multiply by 2 we obtain
[tex]9y = 6y + 3.3 \\ 9y - 6y = 3.3 \\ 3y = 3.3 \\ y = 1.1[/tex]
hence, y = 1.1, so the length of the shorter pipe is 1.1 meter