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Finding the Fourth Proportional to 729.02, 1,006.01 and 414.30

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Solution

The fourth proportional to 729.02, 1,006.01 and 414.30 is: 571.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.02 : 1,006.01 = 414.30 : x
  2. Step 2: Convert to fraction form
    729.02/1,006.01 = 414.30/x
  3. Step 3: Cross multiply
    729.02x = 1,006.01 × 414.30
  4. Step 4: Simplify right side
    729.02x = 416,784.91
  5. Step 5: Solve for x
    x = 416,784.91/729.02
  6. Step 6: Final answer
    x = 571.71

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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.