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Finding the Third Proportional to 77,884 and 122,016

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Solution

The third proportional to 77,884 and 122,016 is: 191,154.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,884 : 122,016 = 122,016 : x
  2. Step 2: Convert to fraction form
    77,884/122,016 = 122,016/x
  3. Step 3: Cross multiply
    77,884x = 122,016 × 122,016
  4. Step 4: Simplify right side
    77,884x = 14,887,904,256
  5. Step 5: Solve for x
    x = 14,887,904,256/77,884
  6. Step 6: Final answer
    x = 191,154.85

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.