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Finding the Third Proportional to 729 and 1,689

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Solution

The third proportional to 729 and 1,689 is: 3,913.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,689 = 1,689 : x
  2. Step 2: Convert to fraction form
    729/1,689 = 1,689/x
  3. Step 3: Cross multiply
    729x = 1,689 × 1,689
  4. Step 4: Simplify right side
    729x = 2,852,721
  5. Step 5: Solve for x
    x = 2,852,721/729
  6. Step 6: Final answer
    x = 3,913.20

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.