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Finding the Third Proportional to 463.78 and 565.03

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Solution

The third proportional to 463.78 and 565.03 is: 688.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    463.78 : 565.03 = 565.03 : x
  2. Step 2: Convert to fraction form
    463.78/565.03 = 565.03/x
  3. Step 3: Cross multiply
    463.78x = 565.03 × 565.03
  4. Step 4: Simplify right side
    463.78x = 319,260.31
  5. Step 5: Solve for x
    x = 319,260.31/463.78
  6. Step 6: Final answer
    x = 688.39

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.