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Finding the Third Proportional to 489,137 and 643,214

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Solution

The third proportional to 489,137 and 643,214 is: 845,824.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    489,137 : 643,214 = 643,214 : x
  2. Step 2: Convert to fraction form
    489,137/643,214 = 643,214/x
  3. Step 3: Cross multiply
    489,137x = 643,214 × 643,214
  4. Step 4: Simplify right side
    489,137x = 413,724,249,796
  5. Step 5: Solve for x
    x = 413,724,249,796/489,137
  6. Step 6: Final answer
    x = 845,824.89

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.