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Finding the Fourth Proportional to 1,098, 1,647 and 414

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Solution

The fourth proportional to 1,098, 1,647 and 414 is: 621

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,098 : 1,647 = 414 : x
  2. Step 2: Convert to fraction form
    1,098/1,647 = 414/x
  3. Step 3: Cross multiply
    1,098x = 1,647 × 414
  4. Step 4: Simplify right side
    1,098x = 681,858
  5. Step 5: Solve for x
    x = 681,858/1,098
  6. Step 6: Final answer
    x = 621

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.