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Finding the Fourth Proportional to 1,106.73, 1,660.10 and 413.57

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Solution

The fourth proportional to 1,106.73, 1,660.10 and 413.57 is: 620.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.73 : 1,660.10 = 413.57 : x
  2. Step 2: Convert to fraction form
    1,106.73/1,660.10 = 413.57/x
  3. Step 3: Cross multiply
    1,106.73x = 1,660.10 × 413.57
  4. Step 4: Simplify right side
    1,106.73x = 686,557.19
  5. Step 5: Solve for x
    x = 686,557.19/1,106.73
  6. Step 6: Final answer
    x = 620.35

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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.