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Finding the Fourth Proportional to 687.82, 1,031.21 and 413.84

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Solution

The fourth proportional to 687.82, 1,031.21 and 413.84 is: 620.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    687.82 : 1,031.21 = 413.84 : x
  2. Step 2: Convert to fraction form
    687.82/1,031.21 = 413.84/x
  3. Step 3: Cross multiply
    687.82x = 1,031.21 × 413.84
  4. Step 4: Simplify right side
    687.82x = 426,760.59
  5. Step 5: Solve for x
    x = 426,760.59/687.82
  6. Step 6: Final answer
    x = 620.46

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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.