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Finding the Third Proportional to 206,397 and 421,541

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Solution

The third proportional to 206,397 and 421,541 is: 860,946.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,397 : 421,541 = 421,541 : x
  2. Step 2: Convert to fraction form
    206,397/421,541 = 421,541/x
  3. Step 3: Cross multiply
    206,397x = 421,541 × 421,541
  4. Step 4: Simplify right side
    206,397x = 177,696,814,681
  5. Step 5: Solve for x
    x = 177,696,814,681/206,397
  6. Step 6: Final answer
    x = 860,946.69

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.