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Finding the Third Proportional to 106,816 and 231,164

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Solution

The third proportional to 106,816 and 231,164 is: 500,269.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,816 : 231,164 = 231,164 : x
  2. Step 2: Convert to fraction form
    106,816/231,164 = 231,164/x
  3. Step 3: Cross multiply
    106,816x = 231,164 × 231,164
  4. Step 4: Simplify right side
    106,816x = 53,436,794,896
  5. Step 5: Solve for x
    x = 53,436,794,896/106,816
  6. Step 6: Final answer
    x = 500,269.57

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.