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Finding the Third Proportional to 299,691 and 421,569

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Solution

The third proportional to 299,691 and 421,569 is: 593,012.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    299,691 : 421,569 = 421,569 : x
  2. Step 2: Convert to fraction form
    299,691/421,569 = 421,569/x
  3. Step 3: Cross multiply
    299,691x = 421,569 × 421,569
  4. Step 4: Simplify right side
    299,691x = 177,720,421,761
  5. Step 5: Solve for x
    x = 177,720,421,761/299,691
  6. Step 6: Final answer
    x = 593,012.21

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.