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Finding the Third Proportional to 412,098 and 869,214

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Solution

The third proportional to 412,098 and 869,214 is: 1,833,381.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,098 : 869,214 = 869,214 : x
  2. Step 2: Convert to fraction form
    412,098/869,214 = 869,214/x
  3. Step 3: Cross multiply
    412,098x = 869,214 × 869,214
  4. Step 4: Simplify right side
    412,098x = 755,532,977,796
  5. Step 5: Solve for x
    x = 755,532,977,796/412,098
  6. Step 6: Final answer
    x = 1,833,381.81

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.