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Finding the Fourth Proportional to 465.09, 698.43 and 413.15

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Solution

The fourth proportional to 465.09, 698.43 and 413.15 is: 620.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    465.09 : 698.43 = 413.15 : x
  2. Step 2: Convert to fraction form
    465.09/698.43 = 413.15/x
  3. Step 3: Cross multiply
    465.09x = 698.43 × 413.15
  4. Step 4: Simplify right side
    465.09x = 288,556.35
  5. Step 5: Solve for x
    x = 288,556.35/465.09
  6. Step 6: Final answer
    x = 620.43

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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.