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Finding the Third Proportional to 102,069 and 209,322

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Solution

The third proportional to 102,069 and 209,322 is: 429,275.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,069 : 209,322 = 209,322 : x
  2. Step 2: Convert to fraction form
    102,069/209,322 = 209,322/x
  3. Step 3: Cross multiply
    102,069x = 209,322 × 209,322
  4. Step 4: Simplify right side
    102,069x = 43,815,699,684
  5. Step 5: Solve for x
    x = 43,815,699,684/102,069
  6. Step 6: Final answer
    x = 429,275.29

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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.