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Finding the Fourth Proportional to 419.52, 578.40 and 413.76

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Solution

The fourth proportional to 419.52, 578.40 and 413.76 is: 570.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.52 : 578.40 = 413.76 : x
  2. Step 2: Convert to fraction form
    419.52/578.40 = 413.76/x
  3. Step 3: Cross multiply
    419.52x = 578.40 × 413.76
  4. Step 4: Simplify right side
    419.52x = 239,318.78
  5. Step 5: Solve for x
    x = 239,318.78/419.52
  6. Step 6: Final answer
    x = 570.46

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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.