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Finding the Third Proportional to 31,991 and 66,031

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Solution

The third proportional to 31,991 and 66,031 is: 136,291.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,991 : 66,031 = 66,031 : x
  2. Step 2: Convert to fraction form
    31,991/66,031 = 66,031/x
  3. Step 3: Cross multiply
    31,991x = 66,031 × 66,031
  4. Step 4: Simplify right side
    31,991x = 4,360,092,961
  5. Step 5: Solve for x
    x = 4,360,092,961/31,991
  6. Step 6: Final answer
    x = 136,291.24

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.