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Finding the Fourth Proportional to 728.58, 1,005.14 and 413.76

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Solution

The fourth proportional to 728.58, 1,005.14 and 413.76 is: 570.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    728.58 : 1,005.14 = 413.76 : x
  2. Step 2: Convert to fraction form
    728.58/1,005.14 = 413.76/x
  3. Step 3: Cross multiply
    728.58x = 1,005.14 × 413.76
  4. Step 4: Simplify right side
    728.58x = 415,886.73
  5. Step 5: Solve for x
    x = 415,886.73/728.58
  6. Step 6: Final answer
    x = 570.82

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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.