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Finding the Fourth Proportional to 688.07, 1,032.23 and 413.80

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Solution

The fourth proportional to 688.07, 1,032.23 and 413.80 is: 620.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    688.07 : 1,032.23 = 413.80 : x
  2. Step 2: Convert to fraction form
    688.07/1,032.23 = 413.80/x
  3. Step 3: Cross multiply
    688.07x = 1,032.23 × 413.80
  4. Step 4: Simplify right side
    688.07x = 427,136.77
  5. Step 5: Solve for x
    x = 427,136.77/688.07
  6. Step 6: Final answer
    x = 620.78

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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.