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Finding the Third Proportional to 8,142 and 15,906

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Solution

The third proportional to 8,142 and 15,906 is: 31,073.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,142 : 15,906 = 15,906 : x
  2. Step 2: Convert to fraction form
    8,142/15,906 = 15,906/x
  3. Step 3: Cross multiply
    8,142x = 15,906 × 15,906
  4. Step 4: Simplify right side
    8,142x = 253,000,836
  5. Step 5: Solve for x
    x = 253,000,836/8,142
  6. Step 6: Final answer
    x = 31,073.55

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.