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Finding the Third Proportional to 77,769 and 209,493

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Solution

The third proportional to 77,769 and 209,493 is: 564,329.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,769 : 209,493 = 209,493 : x
  2. Step 2: Convert to fraction form
    77,769/209,493 = 209,493/x
  3. Step 3: Cross multiply
    77,769x = 209,493 × 209,493
  4. Step 4: Simplify right side
    77,769x = 43,887,317,049
  5. Step 5: Solve for x
    x = 43,887,317,049/77,769
  6. Step 6: Final answer
    x = 564,329.19

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Why These Related Problems?

These problems maintain the same ratio (2.69) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.