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Finding the Third Proportional to 106,238 and 231,796

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Solution

The third proportional to 106,238 and 231,796 is: 505,745.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,238 : 231,796 = 231,796 : x
  2. Step 2: Convert to fraction form
    106,238/231,796 = 231,796/x
  3. Step 3: Cross multiply
    106,238x = 231,796 × 231,796
  4. Step 4: Simplify right side
    106,238x = 53,729,385,616
  5. Step 5: Solve for x
    x = 53,729,385,616/106,238
  6. Step 6: Final answer
    x = 505,745.45

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.