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Finding the Third Proportional to 413 and 871

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Solution

The third proportional to 413 and 871 is: 1,836.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    413 : 871 = 871 : x
  2. Step 2: Convert to fraction form
    413/871 = 871/x
  3. Step 3: Cross multiply
    413x = 871 × 871
  4. Step 4: Simplify right side
    413x = 758,641
  5. Step 5: Solve for x
    x = 758,641/413
  6. Step 6: Final answer
    x = 1,836.90

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.