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Finding the Third Proportional to 71,538 and 106,461

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Solution

The third proportional to 71,538 and 106,461 is: 158,432.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    71,538 : 106,461 = 106,461 : x
  2. Step 2: Convert to fraction form
    71,538/106,461 = 106,461/x
  3. Step 3: Cross multiply
    71,538x = 106,461 × 106,461
  4. Step 4: Simplify right side
    71,538x = 11,333,944,521
  5. Step 5: Solve for x
    x = 11,333,944,521/71,538
  6. Step 6: Final answer
    x = 158,432.50

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.