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Finding the Third Proportional to 400 and 678

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Solution

The third proportional to 400 and 678 is: 1,149.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    400 : 678 = 678 : x
  2. Step 2: Convert to fraction form
    400/678 = 678/x
  3. Step 3: Cross multiply
    400x = 678 × 678
  4. Step 4: Simplify right side
    400x = 459,684
  5. Step 5: Solve for x
    x = 459,684/400
  6. Step 6: Final answer
    x = 1,149.21

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These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.