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Finding the Third Proportional to 402 and 462.75

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Solution

The third proportional to 402 and 462.75 is: 532.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    402 : 462.75 = 462.75 : x
  2. Step 2: Convert to fraction form
    402/462.75 = 462.75/x
  3. Step 3: Cross multiply
    402x = 462.75 × 462.75
  4. Step 4: Simplify right side
    402x = 214,137.56
  5. Step 5: Solve for x
    x = 214,137.56/402
  6. Step 6: Final answer
    x = 532.68

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Why These Related Problems?

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