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Finding the Third Proportional to 412 and 729

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Solution

The third proportional to 412 and 729 is: 1,289.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 729 = 729 : x
  2. Step 2: Convert to fraction form
    412/729 = 729/x
  3. Step 3: Cross multiply
    412x = 729 × 729
  4. Step 4: Simplify right side
    412x = 531,441
  5. Step 5: Solve for x
    x = 531,441/412
  6. Step 6: Final answer
    x = 1,289.91

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.