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Finding the Third Proportional to 75,413 and 165,769

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Solution

The third proportional to 75,413 and 165,769 is: 364,384.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,413 : 165,769 = 165,769 : x
  2. Step 2: Convert to fraction form
    75,413/165,769 = 165,769/x
  3. Step 3: Cross multiply
    75,413x = 165,769 × 165,769
  4. Step 4: Simplify right side
    75,413x = 27,479,361,361
  5. Step 5: Solve for x
    x = 27,479,361,361/75,413
  6. Step 6: Final answer
    x = 364,384.94

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.