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Finding the Third Proportional to 138,103 and 209,023

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Solution

The third proportional to 138,103 and 209,023 is: 316,362.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    138,103 : 209,023 = 209,023 : x
  2. Step 2: Convert to fraction form
    138,103/209,023 = 209,023/x
  3. Step 3: Cross multiply
    138,103x = 209,023 × 209,023
  4. Step 4: Simplify right side
    138,103x = 43,690,614,529
  5. Step 5: Solve for x
    x = 43,690,614,529/138,103
  6. Step 6: Final answer
    x = 316,362.53

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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.