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Finding the Third Proportional to 31,698 and 68,411

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Solution

The third proportional to 31,698 and 68,411 is: 147,645.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,698 : 68,411 = 68,411 : x
  2. Step 2: Convert to fraction form
    31,698/68,411 = 68,411/x
  3. Step 3: Cross multiply
    31,698x = 68,411 × 68,411
  4. Step 4: Simplify right side
    31,698x = 4,680,064,921
  5. Step 5: Solve for x
    x = 4,680,064,921/31,698
  6. Step 6: Final answer
    x = 147,645.43

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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.