How Can I Solve This Static Equilibrium Problem?

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The discussion revolves around a request for assistance with a static equilibrium problem, where the original poster is struggling to find a solution. The moderators emphasize the need for clearer images or typed content to facilitate better help. Users are encouraged to follow the Homework Help Template for future posts. The thread is closed for moderation due to the quality of the submitted images. Clear communication and proper formatting are essential for effective assistance in problem-solving.
Emanuel0406
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Hello! I was wondering if anyone could give me a hand with the following problem. I am stuck and I don't know how to solve it. You can see attached the problem and my work so far. Thank you very much for your help.
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Thread closed for Moderation...
 
You were already asked once in your other thread to please use better images (or just type your work into the forum window). These images are no better.

https://www.physicsforums.com/threads/static-equilibrium.936574/

Do you have access to a printer/scanner? When you have better images or take the time to type your work into the forum, please re-post a new thread, and be sure to use the Homework Help Template you are provided. Thank you.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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