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Finding the Third Proportional to 103,689 and 146,117

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Solution

The third proportional to 103,689 and 146,117 is: 205,905.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    103,689 : 146,117 = 146,117 : x
  2. Step 2: Convert to fraction form
    103,689/146,117 = 146,117/x
  3. Step 3: Cross multiply
    103,689x = 146,117 × 146,117
  4. Step 4: Simplify right side
    103,689x = 21,350,177,689
  5. Step 5: Solve for x
    x = 21,350,177,689/103,689
  6. Step 6: Final answer
    x = 205,905.91

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.