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Finding the Third Proportional to 1,689 and 1,837

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Solution

The third proportional to 1,689 and 1,837 is: 1,997.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,689 : 1,837 = 1,837 : x
  2. Step 2: Convert to fraction form
    1,689/1,837 = 1,837/x
  3. Step 3: Cross multiply
    1,689x = 1,837 × 1,837
  4. Step 4: Simplify right side
    1,689x = 3,374,569
  5. Step 5: Solve for x
    x = 3,374,569/1,689
  6. Step 6: Final answer
    x = 1,997.97

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.