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Finding the Third Proportional to 53,742 and 106,116

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Solution

The third proportional to 53,742 and 106,116 is: 209,530.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,742 : 106,116 = 106,116 : x
  2. Step 2: Convert to fraction form
    53,742/106,116 = 106,116/x
  3. Step 3: Cross multiply
    53,742x = 106,116 × 106,116
  4. Step 4: Simplify right side
    53,742x = 11,260,605,456
  5. Step 5: Solve for x
    x = 11,260,605,456/53,742
  6. Step 6: Final answer
    x = 209,530.82

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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.