Point P and point q are on the line AB, and AP: Pb = 3:2, AQ: QB = 3:4, PQ = 3, find the length of line AB?

Point P and point q are on the line AB, and AP: Pb = 3:2, AQ: QB = 3:4, PQ = 3, find the length of line AB?

Let AQ = a, Pb = B
(a+3):b=3:2
3b=2a+6
a:(3+b)=3:4
4a=9+3b
3b=4a-9
therefore
2a+6=4a-9
2a=15
a=15/2
b=7
The length of line AB is
15/2+3+7
=17.5