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Finding the Third Proportional to 98,199 and 209,214

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Solution

The third proportional to 98,199 and 209,214 is: 445,732.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    98,199 : 209,214 = 209,214 : x
  2. Step 2: Convert to fraction form
    98,199/209,214 = 209,214/x
  3. Step 3: Cross multiply
    98,199x = 209,214 × 209,214
  4. Step 4: Simplify right side
    98,199x = 43,770,497,796
  5. Step 5: Solve for x
    x = 43,770,497,796/98,199
  6. Step 6: Final answer
    x = 445,732.62

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.