MHB Marbles & Stamps: How Many Did Casey Buy?

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Carey initially bought marbles and gave half to Casey, who then purchased stamps and shared half back with Carey. After Carey used 5 stamps and Casey gave away 11 marbles, the remaining ratios of stamps to marbles for both individuals were established. Specifically, the ratio for Carey was 1:7, while for Casey it was 1:5. The discussion revolves around determining the number of stamps Casey originally bought based on these ratios and the transactions. The problem invites participants to share their attempts or difficulties in solving it.
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I have a question

Carey bought some marbles and gave half of them to Casey. Casey bought some stamps and gave half of them to Carey. Carey used 5 stamps and Casey gave away 11 marbles. The ratio of the number of stamps to the number of marbles Carey had left then became 1 : 7 and the ratio of the number of stamps to the number of marbles Casey had left became 1 : 5. How many stamps did Casey buy?
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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