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Finding the Fourth Proportional to 1,027, 1,541.14 and 419

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Solution

The fourth proportional to 1,027, 1,541.14 and 419 is: 628.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,027 : 1,541.14 = 419 : x
  2. Step 2: Convert to fraction form
    1,027/1,541.14 = 419/x
  3. Step 3: Cross multiply
    1,027x = 1,541.14 × 419
  4. Step 4: Simplify right side
    1,027x = 645,737.66
  5. Step 5: Solve for x
    x = 645,737.66/1,027
  6. Step 6: Final answer
    x = 628.76

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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.