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Finding the Third Proportional to 53,698 and 106,041

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Solution

The third proportional to 53,698 and 106,041 is: 209,406.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,698 : 106,041 = 106,041 : x
  2. Step 2: Convert to fraction form
    53,698/106,041 = 106,041/x
  3. Step 3: Cross multiply
    53,698x = 106,041 × 106,041
  4. Step 4: Simplify right side
    53,698x = 11,244,693,681
  5. Step 5: Solve for x
    x = 11,244,693,681/53,698
  6. Step 6: Final answer
    x = 209,406.19

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.