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Finding the Fourth Proportional to 729.09, 1,005.89 and 414.33

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Solution

The fourth proportional to 729.09, 1,005.89 and 414.33 is: 571.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.09 : 1,005.89 = 414.33 : x
  2. Step 2: Convert to fraction form
    729.09/1,005.89 = 414.33/x
  3. Step 3: Cross multiply
    729.09x = 1,005.89 × 414.33
  4. Step 4: Simplify right side
    729.09x = 416,770.40
  5. Step 5: Solve for x
    x = 416,770.40/729.09
  6. Step 6: Final answer
    x = 571.63

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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.