Points P and Q are on line segment AB, and both points are on the same side of the midpoint M of AB. Point P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ = 2, then what is the length of AB?

AP = (AB) and AQ =
(AB).
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so the positions as shown above are correct.
(AB) –
(AB) = 2
→ 35 · (
(AB) –
(AB)) = 35 · 2
→ 5 · 3(AB) – 7 · 2(AB) = 35 · 2
→ 15(AB) – 14(AB) = 70
→ AB = 70.


→ 5 · 3(AB) – 7 · 2(AB) = 35 · 2
→ 15(AB) – 14(AB) = 70
→ AB = 70.