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Finding the Third Proportional to 205,202 and 442,012

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Solution

The third proportional to 205,202 and 442,012 is: 952,108.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,202 : 442,012 = 442,012 : x
  2. Step 2: Convert to fraction form
    205,202/442,012 = 442,012/x
  3. Step 3: Cross multiply
    205,202x = 442,012 × 442,012
  4. Step 4: Simplify right side
    205,202x = 195,374,608,144
  5. Step 5: Solve for x
    x = 195,374,608,144/205,202
  6. Step 6: Final answer
    x = 952,108.69

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.