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Finding the Third Proportional to 30,978 and 65,952

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Solution

The third proportional to 30,978 and 65,952 is: 140,411.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,978 : 65,952 = 65,952 : x
  2. Step 2: Convert to fraction form
    30,978/65,952 = 65,952/x
  3. Step 3: Cross multiply
    30,978x = 65,952 × 65,952
  4. Step 4: Simplify right side
    30,978x = 4,349,666,304
  5. Step 5: Solve for x
    x = 4,349,666,304/30,978
  6. Step 6: Final answer
    x = 140,411.46

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.