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Finding the Third Proportional to 729 and 1,580

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Solution

The third proportional to 729 and 1,580 is: 3,424.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,580 = 1,580 : x
  2. Step 2: Convert to fraction form
    729/1,580 = 1,580/x
  3. Step 3: Cross multiply
    729x = 1,580 × 1,580
  4. Step 4: Simplify right side
    729x = 2,496,400
  5. Step 5: Solve for x
    x = 2,496,400/729
  6. Step 6: Final answer
    x = 3,424.42

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.