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Finding the Third Proportional to 75,714 and 106,166

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Solution

The third proportional to 75,714 and 106,166 is: 148,865.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,714 : 106,166 = 106,166 : x
  2. Step 2: Convert to fraction form
    75,714/106,166 = 106,166/x
  3. Step 3: Cross multiply
    75,714x = 106,166 × 106,166
  4. Step 4: Simplify right side
    75,714x = 11,271,219,556
  5. Step 5: Solve for x
    x = 11,271,219,556/75,714
  6. Step 6: Final answer
    x = 148,865.73

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.