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Finding the Fourth Proportional to 277.42, 413.86 and 257.78

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Solution

The fourth proportional to 277.42, 413.86 and 257.78 is: 384.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    277.42 : 413.86 = 257.78 : x
  2. Step 2: Convert to fraction form
    277.42/413.86 = 257.78/x
  3. Step 3: Cross multiply
    277.42x = 413.86 × 257.78
  4. Step 4: Simplify right side
    277.42x = 106,684.83
  5. Step 5: Solve for x
    x = 106,684.83/277.42
  6. Step 6: Final answer
    x = 384.56

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.