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Finding the Third Proportional to 102,378 and 209,814

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Solution

The third proportional to 102,378 and 209,814 is: 429,993.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,378 : 209,814 = 209,814 : x
  2. Step 2: Convert to fraction form
    102,378/209,814 = 209,814/x
  3. Step 3: Cross multiply
    102,378x = 209,814 × 209,814
  4. Step 4: Simplify right side
    102,378x = 44,021,914,596
  5. Step 5: Solve for x
    x = 44,021,914,596/102,378
  6. Step 6: Final answer
    x = 429,993.89

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.