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Finding the Third Proportional to 209 and 413

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Solution

The third proportional to 209 and 413 is: 816.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 413 = 413 : x
  2. Step 2: Convert to fraction form
    209/413 = 413/x
  3. Step 3: Cross multiply
    209x = 413 × 413
  4. Step 4: Simplify right side
    209x = 170,569
  5. Step 5: Solve for x
    x = 170,569/209
  6. Step 6: Final answer
    x = 816.12

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Why These Related Problems?

These problems maintain the same ratio (1.98) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.