Question 1163136
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There are many methods for solving a problem like this, and many variations of some of those methods.  Here is how I would solve the problem informally.<br>
The first cut cuts the rope into 3 pieces in the ratio 1:4:5 (10 "parts").<br>
The second cut cuts the longest of those 3 parts in the ratio 2:4:3 (9 "parts").<br>
So rewrite the first ratio using 10*9 = 90 parts.  1:4:5 --> 9:36:45.<br>
Now divide the 45 into the ratio 2:4:3.  2:4:3 --> 10:20:15<br>
And now we have 5 pieces of rope of lengths 9, 36, 10, 20, and 15.<br>
In order of lengths, that is 9, 10, 15, 20, and 36.<br>
ANSWER: The ratio of shortest to second longest is 9:20.<br>
Note the given length of the shortest piece is irrelevant, because the question is about the ratio of the lengths of two pieces -- no about the lengths of any pieces.<br>