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Finding the Fourth Proportional to 727.97, 1,004.73 and 413.22

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Solution

The fourth proportional to 727.97, 1,004.73 and 413.22 is: 570.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    727.97 : 1,004.73 = 413.22 : x
  2. Step 2: Convert to fraction form
    727.97/1,004.73 = 413.22/x
  3. Step 3: Cross multiply
    727.97x = 1,004.73 × 413.22
  4. Step 4: Simplify right side
    727.97x = 415,174.53
  5. Step 5: Solve for x
    x = 415,174.53/727.97
  6. Step 6: Final answer
    x = 570.32

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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.