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Finding the Third Proportional to 259 and 413

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Solution

The third proportional to 259 and 413 is: 658.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 413 = 413 : x
  2. Step 2: Convert to fraction form
    259/413 = 413/x
  3. Step 3: Cross multiply
    259x = 413 × 413
  4. Step 4: Simplify right side
    259x = 170,569
  5. Step 5: Solve for x
    x = 170,569/259
  6. Step 6: Final answer
    x = 658.57

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.