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Finding the Fourth Proportional to 686.77, 1,030.17 and 413.09

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Solution

The fourth proportional to 686.77, 1,030.17 and 413.09 is: 619.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.77 : 1,030.17 = 413.09 : x
  2. Step 2: Convert to fraction form
    686.77/1,030.17 = 413.09/x
  3. Step 3: Cross multiply
    686.77x = 1,030.17 × 413.09
  4. Step 4: Simplify right side
    686.77x = 425,552.93
  5. Step 5: Solve for x
    x = 425,552.93/686.77
  6. Step 6: Final answer
    x = 619.64

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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.