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Finding the Third Proportional to 77,854 and 120,412

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Solution

The third proportional to 77,854 and 120,412 is: 186,233.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,854 : 120,412 = 120,412 : x
  2. Step 2: Convert to fraction form
    77,854/120,412 = 120,412/x
  3. Step 3: Cross multiply
    77,854x = 120,412 × 120,412
  4. Step 4: Simplify right side
    77,854x = 14,499,049,744
  5. Step 5: Solve for x
    x = 14,499,049,744/77,854
  6. Step 6: Final answer
    x = 186,233.84

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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.