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Finding the Third Proportional to 1,689 and 3,459

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Solution

The third proportional to 1,689 and 3,459 is: 7,083.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,689 : 3,459 = 3,459 : x
  2. Step 2: Convert to fraction form
    1,689/3,459 = 3,459/x
  3. Step 3: Cross multiply
    1,689x = 3,459 × 3,459
  4. Step 4: Simplify right side
    1,689x = 11,964,681
  5. Step 5: Solve for x
    x = 11,964,681/1,689
  6. Step 6: Final answer
    x = 7,083.88

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.