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Finding the Third Proportional to 105 and 259

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Solution

The third proportional to 105 and 259 is: 638.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    105 : 259 = 259 : x
  2. Step 2: Convert to fraction form
    105/259 = 259/x
  3. Step 3: Cross multiply
    105x = 259 × 259
  4. Step 4: Simplify right side
    105x = 67,081
  5. Step 5: Solve for x
    x = 67,081/105
  6. Step 6: Final answer
    x = 638.87

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Why These Related Problems?

These problems maintain the same ratio (2.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.