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Finding the Third Proportional to 198,209 and 412,834

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Solution

The third proportional to 198,209 and 412,834 is: 859,859.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,209 : 412,834 = 412,834 : x
  2. Step 2: Convert to fraction form
    198,209/412,834 = 412,834/x
  3. Step 3: Cross multiply
    198,209x = 412,834 × 412,834
  4. Step 4: Simplify right side
    198,209x = 170,431,911,556
  5. Step 5: Solve for x
    x = 170,431,911,556/198,209
  6. Step 6: Final answer
    x = 859,859.60

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.