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Finding the Third Proportional to 412 and 567

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Solution

The third proportional to 412 and 567 is: 780.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 567 = 567 : x
  2. Step 2: Convert to fraction form
    412/567 = 567/x
  3. Step 3: Cross multiply
    412x = 567 × 567
  4. Step 4: Simplify right side
    412x = 321,489
  5. Step 5: Solve for x
    x = 321,489/412
  6. Step 6: Final answer
    x = 780.31

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These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.