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Finding the Fourth Proportional to 1,154.09, 1,731.21 and 413.84

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Solution

The fourth proportional to 1,154.09, 1,731.21 and 413.84 is: 620.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,154.09 : 1,731.21 = 413.84 : x
  2. Step 2: Convert to fraction form
    1,154.09/1,731.21 = 413.84/x
  3. Step 3: Cross multiply
    1,154.09x = 1,731.21 × 413.84
  4. Step 4: Simplify right side
    1,154.09x = 716,443.95
  5. Step 5: Solve for x
    x = 716,443.95/1,154.09
  6. Step 6: Final answer
    x = 620.79

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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.