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Finding the Fourth Proportional to 727.93, 1,004.57 and 413.20

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Solution

The fourth proportional to 727.93, 1,004.57 and 413.20 is: 570.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    727.93 : 1,004.57 = 413.20 : x
  2. Step 2: Convert to fraction form
    727.93/1,004.57 = 413.20/x
  3. Step 3: Cross multiply
    727.93x = 1,004.57 × 413.20
  4. Step 4: Simplify right side
    727.93x = 415,088.32
  5. Step 5: Solve for x
    x = 415,088.32/727.93
  6. Step 6: Final answer
    x = 570.23

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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.