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Finding the Fourth Proportional to 729.53, 1,006.70 and 414.80

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Solution

The fourth proportional to 729.53, 1,006.70 and 414.80 is: 572.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.53 : 1,006.70 = 414.80 : x
  2. Step 2: Convert to fraction form
    729.53/1,006.70 = 414.80/x
  3. Step 3: Cross multiply
    729.53x = 1,006.70 × 414.80
  4. Step 4: Simplify right side
    729.53x = 417,572.05
  5. Step 5: Solve for x
    x = 417,572.05/729.53
  6. Step 6: Final answer
    x = 572.39

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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.