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Finding the Third Proportional to 513 and 1,299

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Solution

The third proportional to 513 and 1,299 is: 3,289.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    513 : 1,299 = 1,299 : x
  2. Step 2: Convert to fraction form
    513/1,299 = 1,299/x
  3. Step 3: Cross multiply
    513x = 1,299 × 1,299
  4. Step 4: Simplify right side
    513x = 1,687,401
  5. Step 5: Solve for x
    x = 1,687,401/513
  6. Step 6: Final answer
    x = 3,289.28

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Why These Related Problems?

These problems maintain the same ratio (2.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.