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Finding the Third Proportional to 105.75 and 259.13

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Solution

The third proportional to 105.75 and 259.13 is: 634.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    105.75 : 259.13 = 259.13 : x
  2. Step 2: Convert to fraction form
    105.75/259.13 = 259.13/x
  3. Step 3: Cross multiply
    105.75x = 259.13 × 259.13
  4. Step 4: Simplify right side
    105.75x = 67,145.77
  5. Step 5: Solve for x
    x = 67,145.77/105.75
  6. Step 6: Final answer
    x = 634.95

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Why These Related Problems?

These problems maintain the same ratio (2.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.