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Finding the Third Proportional to 412 and 472

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Solution

The third proportional to 412 and 472 is: 540.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 472 = 472 : x
  2. Step 2: Convert to fraction form
    412/472 = 472/x
  3. Step 3: Cross multiply
    412x = 472 × 472
  4. Step 4: Simplify right side
    412x = 222,784
  5. Step 5: Solve for x
    x = 222,784/412
  6. Step 6: Final answer
    x = 540.74

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These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.