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Finding the Fourth Proportional to 1,509.42, 2,264.24 and 413.70

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Solution

The fourth proportional to 1,509.42, 2,264.24 and 413.70 is: 620.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,509.42 : 2,264.24 = 413.70 : x
  2. Step 2: Convert to fraction form
    1,509.42/2,264.24 = 413.70/x
  3. Step 3: Cross multiply
    1,509.42x = 2,264.24 × 413.70
  4. Step 4: Simplify right side
    1,509.42x = 936,716.09
  5. Step 5: Solve for x
    x = 936,716.09/1,509.42
  6. Step 6: Final answer
    x = 620.58

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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.