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Finding the Third Proportional to 57,769 and 86,416

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Solution

The third proportional to 57,769 and 86,416 is: 129,268.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    57,769 : 86,416 = 86,416 : x
  2. Step 2: Convert to fraction form
    57,769/86,416 = 86,416/x
  3. Step 3: Cross multiply
    57,769x = 86,416 × 86,416
  4. Step 4: Simplify right side
    57,769x = 7,467,725,056
  5. Step 5: Solve for x
    x = 7,467,725,056/57,769
  6. Step 6: Final answer
    x = 129,268.73

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.