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Finding the Third Proportional to 729 and 1,026

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Solution

The third proportional to 729 and 1,026 is: 1,444

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,026 = 1,026 : x
  2. Step 2: Convert to fraction form
    729/1,026 = 1,026/x
  3. Step 3: Cross multiply
    729x = 1,026 × 1,026
  4. Step 4: Simplify right side
    729x = 1,052,676
  5. Step 5: Solve for x
    x = 1,052,676/729
  6. Step 6: Final answer
    x = 1,444

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.