SOLUTION: The books to Robins ratio of the number of Claudes is 5:6. The ratio of the number of Robins books to Ian's Books is 7:4. If Claude has 22 books more than Ian, How many books does

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Question 1105242: The books to Robins ratio of the number of Claudes is 5:6. The ratio of the number of Robins books to Ian's Books is 7:4. If Claude has 22 books more than Ian, How many books does Robin have?
Answer by greenestamps(13203) About Me  (Show Source):
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Robin:Claude = 5:6
Robin:Ian = 7:4

Rewrite the two ratios making the numbers for Robin the same in both, using the least common multiple of 5 and 7 (or any common multiple...):

Robin:Claude = 35:42
Robin:Ian = 35:20

Now we can conclude that
Claude:Ian = 42:20

And then, since Claude has 22 more books than Ian, it is clear that in fact Claude has 42 books and Ian has 20.

And that means Robin has 35.