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Finding the Fourth Proportional to 686.06, 1,029.12 and 413.90

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Solution

The fourth proportional to 686.06, 1,029.12 and 413.90 is: 620.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.06 : 1,029.12 = 413.90 : x
  2. Step 2: Convert to fraction form
    686.06/1,029.12 = 413.90/x
  3. Step 3: Cross multiply
    686.06x = 1,029.12 × 413.90
  4. Step 4: Simplify right side
    686.06x = 425,952.77
  5. Step 5: Solve for x
    x = 425,952.77/686.06
  6. Step 6: Final answer
    x = 620.87

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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.