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Finding the Third Proportional to 42,971 and 66,401

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Solution

The third proportional to 42,971 and 66,401 is: 102,606.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,971 : 66,401 = 66,401 : x
  2. Step 2: Convert to fraction form
    42,971/66,401 = 66,401/x
  3. Step 3: Cross multiply
    42,971x = 66,401 × 66,401
  4. Step 4: Simplify right side
    42,971x = 4,409,092,801
  5. Step 5: Solve for x
    x = 4,409,092,801/42,971
  6. Step 6: Final answer
    x = 102,606.24

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.