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Finding the Third Proportional to 413 and 463

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Solution

The third proportional to 413 and 463 is: 519.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    413 : 463 = 463 : x
  2. Step 2: Convert to fraction form
    413/463 = 463/x
  3. Step 3: Cross multiply
    413x = 463 × 463
  4. Step 4: Simplify right side
    413x = 214,369
  5. Step 5: Solve for x
    x = 214,369/413
  6. Step 6: Final answer
    x = 519.05

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.