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Finding the Third Proportional to 75,978 and 197,235

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Solution

The third proportional to 75,978 and 197,235 is: 512,011.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,978 : 197,235 = 197,235 : x
  2. Step 2: Convert to fraction form
    75,978/197,235 = 197,235/x
  3. Step 3: Cross multiply
    75,978x = 197,235 × 197,235
  4. Step 4: Simplify right side
    75,978x = 38,901,645,225
  5. Step 5: Solve for x
    x = 38,901,645,225/75,978
  6. Step 6: Final answer
    x = 512,011.97

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.