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Finding the Third Proportional to 77,856 and 120,414

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Solution

The third proportional to 77,856 and 120,414 is: 186,235.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,856 : 120,414 = 120,414 : x
  2. Step 2: Convert to fraction form
    77,856/120,414 = 120,414/x
  3. Step 3: Cross multiply
    77,856x = 120,414 × 120,414
  4. Step 4: Simplify right side
    77,856x = 14,499,531,396
  5. Step 5: Solve for x
    x = 14,499,531,396/77,856
  6. Step 6: Final answer
    x = 186,235.25

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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.