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Finding the Third Proportional to 697 and 1,683

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Solution

The third proportional to 697 and 1,683 is: 4,063.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    697 : 1,683 = 1,683 : x
  2. Step 2: Convert to fraction form
    697/1,683 = 1,683/x
  3. Step 3: Cross multiply
    697x = 1,683 × 1,683
  4. Step 4: Simplify right side
    697x = 2,832,489
  5. Step 5: Solve for x
    x = 2,832,489/697
  6. Step 6: Final answer
    x = 4,063.83

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.