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Finding the Fourth Proportional to 105.78, 146.09 and 82.40

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Solution

The fourth proportional to 105.78, 146.09 and 82.40 is: 113.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    105.78 : 146.09 = 82.40 : x
  2. Step 2: Convert to fraction form
    105.78/146.09 = 82.40/x
  3. Step 3: Cross multiply
    105.78x = 146.09 × 82.40
  4. Step 4: Simplify right side
    105.78x = 12,036.67
  5. Step 5: Solve for x
    x = 12,036.67/105.78
  6. Step 6: Final answer
    x = 113.79

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.