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Finding the Third Proportional to 509,456 and 765,464

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Solution

The third proportional to 509,456 and 765,464 is: 1,150,119.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    509,456 : 765,464 = 765,464 : x
  2. Step 2: Convert to fraction form
    509,456/765,464 = 765,464/x
  3. Step 3: Cross multiply
    509,456x = 765,464 × 765,464
  4. Step 4: Simplify right side
    509,456x = 585,935,135,296
  5. Step 5: Solve for x
    x = 585,935,135,296/509,456
  6. Step 6: Final answer
    x = 1,150,119.22

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.