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Finding the Third Proportional to 212,382 and 463,401

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Solution

The third proportional to 212,382 and 463,401 is: 1,011,104.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,382 : 463,401 = 463,401 : x
  2. Step 2: Convert to fraction form
    212,382/463,401 = 463,401/x
  3. Step 3: Cross multiply
    212,382x = 463,401 × 463,401
  4. Step 4: Simplify right side
    212,382x = 214,740,486,801
  5. Step 5: Solve for x
    x = 214,740,486,801/212,382
  6. Step 6: Final answer
    x = 1,011,104.93

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.