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Finding the Third Proportional to 51,998 and 106,460

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Solution

The third proportional to 51,998 and 106,460 is: 217,964.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,998 : 106,460 = 106,460 : x
  2. Step 2: Convert to fraction form
    51,998/106,460 = 106,460/x
  3. Step 3: Cross multiply
    51,998x = 106,460 × 106,460
  4. Step 4: Simplify right side
    51,998x = 11,333,731,600
  5. Step 5: Solve for x
    x = 11,333,731,600/51,998
  6. Step 6: Final answer
    x = 217,964.76

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.