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Finding the Third Proportional to 827 and 2,171

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Solution

The third proportional to 827 and 2,171 is: 5,699.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    827 : 2,171 = 2,171 : x
  2. Step 2: Convert to fraction form
    827/2,171 = 2,171/x
  3. Step 3: Cross multiply
    827x = 2,171 × 2,171
  4. Step 4: Simplify right side
    827x = 4,713,241
  5. Step 5: Solve for x
    x = 4,713,241/827
  6. Step 6: Final answer
    x = 5,699.20

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Why These Related Problems?

These problems maintain the same ratio (2.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.