Troubleshooting a Two Mass Interaction Problem in Scientific Research

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The discussion revolves around difficulties in solving equations related to a two mass interaction problem in scientific research. The poster is struggling to satisfy the equations and is unsure if they have provided all necessary information. They express frustration over the unresolved issue and seek feedback on whether anything is missing from their post. The attachment is intended to contain all relevant details for troubleshooting. Clarification on the equations or additional context may be needed to assist in resolving the problem.
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All the information is in the attachment.
The problem I'm having is that I can't seem to satisfy the equations correctly, and I can't figure out why. Am I doing this right?
 

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Is there something missing in my post? I'm pretty sure I gave all the information in the attachment but let me know if I need to change something. This problem is really bothering me.
 
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