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Finding the Fourth Proportional to 729.78, 1,006.92 and 419.28

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Solution

The fourth proportional to 729.78, 1,006.92 and 419.28 is: 578.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.78 : 1,006.92 = 419.28 : x
  2. Step 2: Convert to fraction form
    729.78/1,006.92 = 419.28/x
  3. Step 3: Cross multiply
    729.78x = 1,006.92 × 419.28
  4. Step 4: Simplify right side
    729.78x = 422,181.42
  5. Step 5: Solve for x
    x = 422,181.42/729.78
  6. Step 6: Final answer
    x = 578.51

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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.