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Finding the Third Proportional to 65,978 and 138,437

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Solution

The third proportional to 65,978 and 138,437 is: 290,472.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,978 : 138,437 = 138,437 : x
  2. Step 2: Convert to fraction form
    65,978/138,437 = 138,437/x
  3. Step 3: Cross multiply
    65,978x = 138,437 × 138,437
  4. Step 4: Simplify right side
    65,978x = 19,164,802,969
  5. Step 5: Solve for x
    x = 19,164,802,969/65,978
  6. Step 6: Final answer
    x = 290,472.63

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These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.