A renewable energy facility distributes stored electricity among three battery banks: Bank 1, Bank 2, and Bank 3. Initially, the ratio of the energy stored in Bank 1 to Bank 2 to Bank 3 is .
To balance the system, two sequential transfers of energy are performed without any energy loss:
1. Energy is transferred from Bank 3 to Bank 1 such that the ratio of the energy in Bank 1 to Bank 2 becomes .
2. Energy is then transferred from Bank 2 to Bank 3 such that the ratio of the energy in Bank 2 to Bank 3 becomes .
If Bank 3 contains more energy after the second transfer than it did initially, what was the total amount of energy, in MWh, stored across all three battery banks?
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Cevap
The total energy stored across all three battery banks is .
The correct answer is . By setting up algebraic expressions for the energy in each bank relative to total energy , we track how each transfer modifies individual bank totals while conserving total energy. The intermediate transfer reduces Bank 3 from to , and the subsequent transfer increases it to . The resulting difference of equals , solving directly to .
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Anahtar Kavram
Multi-stage ratio rebalancing and conservation of total quantity