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Finding the Third Proportional to 262,569 and 289,638

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Solution

The third proportional to 262,569 and 289,638 is: 319,497.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,569 : 289,638 = 289,638 : x
  2. Step 2: Convert to fraction form
    262,569/289,638 = 289,638/x
  3. Step 3: Cross multiply
    262,569x = 289,638 × 289,638
  4. Step 4: Simplify right side
    262,569x = 83,890,171,044
  5. Step 5: Solve for x
    x = 83,890,171,044/262,569
  6. Step 6: Final answer
    x = 319,497.62

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.