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Finding the Third Proportional to 408 and 523.50

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Solution

The third proportional to 408 and 523.50 is: 671.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    408 : 523.50 = 523.50 : x
  2. Step 2: Convert to fraction form
    408/523.50 = 523.50/x
  3. Step 3: Cross multiply
    408x = 523.50 × 523.50
  4. Step 4: Simplify right side
    408x = 274,052.25
  5. Step 5: Solve for x
    x = 274,052.25/408
  6. Step 6: Final answer
    x = 671.70

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.