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Finding the Fourth Proportional to 727.82, 1,004.22 and 413.02

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Solution

The fourth proportional to 727.82, 1,004.22 and 413.02 is: 569.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    727.82 : 1,004.22 = 413.02 : x
  2. Step 2: Convert to fraction form
    727.82/1,004.22 = 413.02/x
  3. Step 3: Cross multiply
    727.82x = 1,004.22 × 413.02
  4. Step 4: Simplify right side
    727.82x = 414,761.83
  5. Step 5: Solve for x
    x = 414,761.83/727.82
  6. Step 6: Final answer
    x = 569.87

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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.