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Finding the Third Proportional to 206,966 and 312,069

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Solution

The third proportional to 206,966 and 312,069 is: 470,546.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,966 : 312,069 = 312,069 : x
  2. Step 2: Convert to fraction form
    206,966/312,069 = 312,069/x
  3. Step 3: Cross multiply
    206,966x = 312,069 × 312,069
  4. Step 4: Simplify right side
    206,966x = 97,387,060,761
  5. Step 5: Solve for x
    x = 97,387,060,761/206,966
  6. Step 6: Final answer
    x = 470,546.18

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.