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Finding the Third Proportional to 31,986 and 51,102

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Solution

The third proportional to 31,986 and 51,102 is: 81,642.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,986 : 51,102 = 51,102 : x
  2. Step 2: Convert to fraction form
    31,986/51,102 = 51,102/x
  3. Step 3: Cross multiply
    31,986x = 51,102 × 51,102
  4. Step 4: Simplify right side
    31,986x = 2,611,414,404
  5. Step 5: Solve for x
    x = 2,611,414,404/31,986
  6. Step 6: Final answer
    x = 81,642.42

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.