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Finding the Third Proportional to 827 and 1,706

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Solution

The third proportional to 827 and 1,706 is: 3,519.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    827 : 1,706 = 1,706 : x
  2. Step 2: Convert to fraction form
    827/1,706 = 1,706/x
  3. Step 3: Cross multiply
    827x = 1,706 × 1,706
  4. Step 4: Simplify right side
    827x = 2,910,436
  5. Step 5: Solve for x
    x = 2,910,436/827
  6. Step 6: Final answer
    x = 3,519.27

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.