math question

1.if 4x-5y=0, find(3x-y):(2x+3y)
Solve:
4x-5y=0
4x=5y
x:y=5:4
Let x=5k, y=4k.
(3x-y):(2x+3y)
=(15k-4k):(10k+12k)
=11k:22k
=1/2

2.if 2x=3y=4z,find(x-y+z):(x+y-z)
Solve:
2x=3y
x:y=3:2=6:4
3y=4z
y:z=4:3
So, x:y:z=6:4:3
Let x=6k, y=4k, z=3k.
(x-y+z):(x+y-z)
=(6k-4k+3k):(6k+4k-3k)
=5k:7k
=5/7

3.if a:b=2:3 and b:c=4:5,find(3a-b):(b+2c)
Solve:
a:b=2:3=8:12
b:c=4:5=12:15
So, a:b:c=8:12:15
Let a=8k, b=12k, c=15k.
(3a-b):(b+2c)
=(24k-12k):(12k+30k)
=12k:42k
=2/7

4.if a:b=3:5 and b:c=3:2,find (2a+3b-c)/(3a-2b+c)
Solve:
a:b=3:5=9:15
b:c=3:2=15:10
So, a:b:c=9:15:10
Let a=9k, b=15k, c=10k
(2a+3b-c)/(3a-2b+c)
=(18k+45k-10k)/(27k-30k+10k)
=53k/20k
=53/20