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Finding the Third Proportional to 312 and 398

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Solution

The third proportional to 312 and 398 is: 507.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    312 : 398 = 398 : x
  2. Step 2: Convert to fraction form
    312/398 = 398/x
  3. Step 3: Cross multiply
    312x = 398 × 398
  4. Step 4: Simplify right side
    312x = 158,404
  5. Step 5: Solve for x
    x = 158,404/312
  6. Step 6: Final answer
    x = 507.71

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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.