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Finding the Third Proportional to 31,878 and 40,419

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Solution

The third proportional to 31,878 and 40,419 is: 51,248.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,878 : 40,419 = 40,419 : x
  2. Step 2: Convert to fraction form
    31,878/40,419 = 40,419/x
  3. Step 3: Cross multiply
    31,878x = 40,419 × 40,419
  4. Step 4: Simplify right side
    31,878x = 1,633,695,561
  5. Step 5: Solve for x
    x = 1,633,695,561/31,878
  6. Step 6: Final answer
    x = 51,248.37

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.