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Finding the Third Proportional to 138,102 and 209,021

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Solution

The third proportional to 138,102 and 209,021 is: 316,358.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    138,102 : 209,021 = 209,021 : x
  2. Step 2: Convert to fraction form
    138,102/209,021 = 209,021/x
  3. Step 3: Cross multiply
    138,102x = 209,021 × 209,021
  4. Step 4: Simplify right side
    138,102x = 43,689,778,441
  5. Step 5: Solve for x
    x = 43,689,778,441/138,102
  6. Step 6: Final answer
    x = 316,358.77

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.