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Finding the Third Proportional to 102,022 and 209,202

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Solution

The third proportional to 102,022 and 209,202 is: 428,980.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,022 : 209,202 = 209,202 : x
  2. Step 2: Convert to fraction form
    102,022/209,202 = 209,202/x
  3. Step 3: Cross multiply
    102,022x = 209,202 × 209,202
  4. Step 4: Simplify right side
    102,022x = 43,765,476,804
  5. Step 5: Solve for x
    x = 43,765,476,804/102,022
  6. Step 6: Final answer
    x = 428,980.78

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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.