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Finding the Third Proportional to 106,024 and 231,464

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Solution

The third proportional to 106,024 and 231,464 is: 505,315.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,024 : 231,464 = 231,464 : x
  2. Step 2: Convert to fraction form
    106,024/231,464 = 231,464/x
  3. Step 3: Cross multiply
    106,024x = 231,464 × 231,464
  4. Step 4: Simplify right side
    106,024x = 53,575,583,296
  5. Step 5: Solve for x
    x = 53,575,583,296/106,024
  6. Step 6: Final answer
    x = 505,315.62

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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.