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Finding the Third Proportional to 31,678 and 68,432

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Solution

The third proportional to 31,678 and 68,432 is: 147,829.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,678 : 68,432 = 68,432 : x
  2. Step 2: Convert to fraction form
    31,678/68,432 = 68,432/x
  3. Step 3: Cross multiply
    31,678x = 68,432 × 68,432
  4. Step 4: Simplify right side
    31,678x = 4,682,938,624
  5. Step 5: Solve for x
    x = 4,682,938,624/31,678
  6. Step 6: Final answer
    x = 147,829.36

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.