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Finding the Third Proportional to 729 and 1,540.13

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Solution

The third proportional to 729 and 1,540.13 is: 3,253.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,540.13 = 1,540.13 : x
  2. Step 2: Convert to fraction form
    729/1,540.13 = 1,540.13/x
  3. Step 3: Cross multiply
    729x = 1,540.13 × 1,540.13
  4. Step 4: Simplify right side
    729x = 2,371,985.02
  5. Step 5: Solve for x
    x = 2,371,985.02/729
  6. Step 6: Final answer
    x = 3,253.75

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.