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Finding the Fourth Proportional to 520.65, 782.06 and 413.19

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Solution

The fourth proportional to 520.65, 782.06 and 413.19 is: 620.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    520.65 : 782.06 = 413.19 : x
  2. Step 2: Convert to fraction form
    520.65/782.06 = 413.19/x
  3. Step 3: Cross multiply
    520.65x = 782.06 × 413.19
  4. Step 4: Simplify right side
    520.65x = 323,137.31
  5. Step 5: Solve for x
    x = 323,137.31/520.65
  6. Step 6: Final answer
    x = 620.64

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.