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Finding the Fourth Proportional to 729.40, 1,006.50 and 414.66

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Solution

The fourth proportional to 729.40, 1,006.50 and 414.66 is: 572.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.40 : 1,006.50 = 414.66 : x
  2. Step 2: Convert to fraction form
    729.40/1,006.50 = 414.66/x
  3. Step 3: Cross multiply
    729.40x = 1,006.50 × 414.66
  4. Step 4: Simplify right side
    729.40x = 417,355.29
  5. Step 5: Solve for x
    x = 417,355.29/729.40
  6. Step 6: Final answer
    x = 572.19

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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.