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Finding the Third Proportional to 417 and 829

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Solution

The third proportional to 417 and 829 is: 1,648.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    417 : 829 = 829 : x
  2. Step 2: Convert to fraction form
    417/829 = 829/x
  3. Step 3: Cross multiply
    417x = 829 × 829
  4. Step 4: Simplify right side
    417x = 687,241
  5. Step 5: Solve for x
    x = 687,241/417
  6. Step 6: Final answer
    x = 1,648.06

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Why These Related Problems?

These problems maintain the same ratio (1.99) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.