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Finding the Fourth Proportional to 728.42, 1,005.24 and 413.72

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Solution

The fourth proportional to 728.42, 1,005.24 and 413.72 is: 570.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    728.42 : 1,005.24 = 413.72 : x
  2. Step 2: Convert to fraction form
    728.42/1,005.24 = 413.72/x
  3. Step 3: Cross multiply
    728.42x = 1,005.24 × 413.72
  4. Step 4: Simplify right side
    728.42x = 415,888.19
  5. Step 5: Solve for x
    x = 415,888.19/728.42
  6. Step 6: Final answer
    x = 570.95

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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.