If P and Q are on the line AB, AP: Pb = 2:3, AQ: QB = 3:4, and PQ = 3, the length of AB is obtained

Let AP = 2A, Pb = 3A, AQ = 3b, QB = 4B,
AQ-AP=PQ:3b-2a=3
2a+3a=3b+4b
Two equations can be derived
a=21,b=15
AB=5a=105

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