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Finding the Third Proportional to 43,414 and 65,109

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Solution

The third proportional to 43,414 and 65,109 is: 97,645.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    43,414 : 65,109 = 65,109 : x
  2. Step 2: Convert to fraction form
    43,414/65,109 = 65,109/x
  3. Step 3: Cross multiply
    43,414x = 65,109 × 65,109
  4. Step 4: Simplify right side
    43,414x = 4,239,181,881
  5. Step 5: Solve for x
    x = 4,239,181,881/43,414
  6. Step 6: Final answer
    x = 97,645.50

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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.