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Finding the Fourth Proportional to 727.83, 1,004.40 and 413.09

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Solution

The fourth proportional to 727.83, 1,004.40 and 413.09 is: 570.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    727.83 : 1,004.40 = 413.09 : x
  2. Step 2: Convert to fraction form
    727.83/1,004.40 = 413.09/x
  3. Step 3: Cross multiply
    727.83x = 1,004.40 × 413.09
  4. Step 4: Simplify right side
    727.83x = 414,902.57
  5. Step 5: Solve for x
    x = 414,902.57/727.83
  6. Step 6: Final answer
    x = 570.05

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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.