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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So what is the problem? Have you tried anything? Post your attempt (or at least something which explains your difficulty in solving the question).
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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