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Finding the Third Proportional to 106,459 and 233,653

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Solution

The third proportional to 106,459 and 233,653 is: 512,814.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,459 : 233,653 = 233,653 : x
  2. Step 2: Convert to fraction form
    106,459/233,653 = 233,653/x
  3. Step 3: Cross multiply
    106,459x = 233,653 × 233,653
  4. Step 4: Simplify right side
    106,459x = 54,593,724,409
  5. Step 5: Solve for x
    x = 54,593,724,409/106,459
  6. Step 6: Final answer
    x = 512,814.55

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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.