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Finding the Third Proportional to 205,229 and 296,967

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Solution

The third proportional to 205,229 and 296,967 is: 429,712.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,229 : 296,967 = 296,967 : x
  2. Step 2: Convert to fraction form
    205,229/296,967 = 296,967/x
  3. Step 3: Cross multiply
    205,229x = 296,967 × 296,967
  4. Step 4: Simplify right side
    205,229x = 88,189,399,089
  5. Step 5: Solve for x
    x = 88,189,399,089/205,229
  6. Step 6: Final answer
    x = 429,712.17

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.