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Finding the Third Proportional to 51,471 and 82,195

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Solution

The third proportional to 51,471 and 82,195 is: 131,258.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,471 : 82,195 = 82,195 : x
  2. Step 2: Convert to fraction form
    51,471/82,195 = 82,195/x
  3. Step 3: Cross multiply
    51,471x = 82,195 × 82,195
  4. Step 4: Simplify right side
    51,471x = 6,756,018,025
  5. Step 5: Solve for x
    x = 6,756,018,025/51,471
  6. Step 6: Final answer
    x = 131,258.73

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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.