Alex, bob, and claudia split 126 cm wire evenly among themselves. they then proceeded to cut their pieces of wire into smaller, equal parts. alex cut his wire 18 times, and kept 7 pieces. bob cut his wire 2 times more than alex did, and kept 9 pieces. while claudia divided her wire into 13 equal parts, and kept only one piece. who kept the longest part of the original wire and what was the length of that part?

If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.

Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.

Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.

Bob kept (3/7)·(1/3)·126 cm = 18 cm.

Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.

Bob kept the longest part of the original wire.

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