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Finding the Third Proportional to 106,209 and 231,741

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Solution

The third proportional to 106,209 and 231,741 is: 505,643.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,209 : 231,741 = 231,741 : x
  2. Step 2: Convert to fraction form
    106,209/231,741 = 231,741/x
  3. Step 3: Cross multiply
    106,209x = 231,741 × 231,741
  4. Step 4: Simplify right side
    106,209x = 53,703,891,081
  5. Step 5: Solve for x
    x = 53,703,891,081/106,209
  6. Step 6: Final answer
    x = 505,643.51

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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.