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Finding the Third Proportional to 301,410 and 410,466

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Solution

The third proportional to 301,410 and 410,466 is: 558,980.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    301,410 : 410,466 = 410,466 : x
  2. Step 2: Convert to fraction form
    301,410/410,466 = 410,466/x
  3. Step 3: Cross multiply
    301,410x = 410,466 × 410,466
  4. Step 4: Simplify right side
    301,410x = 168,482,337,156
  5. Step 5: Solve for x
    x = 168,482,337,156/301,410
  6. Step 6: Final answer
    x = 558,980.58

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.