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Finding the Third Proportional to 106,823 and 233,497

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Solution

The third proportional to 106,823 and 233,497 is: 510,384.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,823 : 233,497 = 233,497 : x
  2. Step 2: Convert to fraction form
    106,823/233,497 = 233,497/x
  3. Step 3: Cross multiply
    106,823x = 233,497 × 233,497
  4. Step 4: Simplify right side
    106,823x = 54,520,849,009
  5. Step 5: Solve for x
    x = 54,520,849,009/106,823
  6. Step 6: Final answer
    x = 510,384.93

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.