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Finding the Fourth Proportional to 729.50, 1,006.71 and 419

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Solution

The fourth proportional to 729.50, 1,006.71 and 419 is: 578.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.50 : 1,006.71 = 419 : x
  2. Step 2: Convert to fraction form
    729.50/1,006.71 = 419/x
  3. Step 3: Cross multiply
    729.50x = 1,006.71 × 419
  4. Step 4: Simplify right side
    729.50x = 421,811.49
  5. Step 5: Solve for x
    x = 421,811.49/729.50
  6. Step 6: Final answer
    x = 578.22

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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.