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Finding the Third Proportional to 397 and 514

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Solution

The third proportional to 397 and 514 is: 665.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    397 : 514 = 514 : x
  2. Step 2: Convert to fraction form
    397/514 = 514/x
  3. Step 3: Cross multiply
    397x = 514 × 514
  4. Step 4: Simplify right side
    397x = 264,196
  5. Step 5: Solve for x
    x = 264,196/397
  6. Step 6: Final answer
    x = 665.48

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Why These Related Problems?

These problems maintain the same ratio (1.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.