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Finding the Fourth Proportional to 1,106.52, 1,660.63 and 413.70

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Solution

The fourth proportional to 1,106.52, 1,660.63 and 413.70 is: 620.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.52 : 1,660.63 = 413.70 : x
  2. Step 2: Convert to fraction form
    1,106.52/1,660.63 = 413.70/x
  3. Step 3: Cross multiply
    1,106.52x = 1,660.63 × 413.70
  4. Step 4: Simplify right side
    1,106.52x = 687,002.63
  5. Step 5: Solve for x
    x = 687,002.63/1,106.52
  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.