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Finding the Third Proportional to 75,409 and 165,762

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Solution

The third proportional to 75,409 and 165,762 is: 364,373.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,409 : 165,762 = 165,762 : x
  2. Step 2: Convert to fraction form
    75,409/165,762 = 165,762/x
  3. Step 3: Cross multiply
    75,409x = 165,762 × 165,762
  4. Step 4: Simplify right side
    75,409x = 27,477,040,644
  5. Step 5: Solve for x
    x = 27,477,040,644/75,409
  6. Step 6: Final answer
    x = 364,373.49

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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.