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Finding the Third Proportional to 102,538 and 221,432

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Solution

The third proportional to 102,538 and 221,432 is: 478,184.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,538 : 221,432 = 221,432 : x
  2. Step 2: Convert to fraction form
    102,538/221,432 = 221,432/x
  3. Step 3: Cross multiply
    102,538x = 221,432 × 221,432
  4. Step 4: Simplify right side
    102,538x = 49,032,130,624
  5. Step 5: Solve for x
    x = 49,032,130,624/102,538
  6. Step 6: Final answer
    x = 478,184.97

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.