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Finding the Fourth Proportional to 1,509.57, 2,264.11 and 413.68

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Solution

The fourth proportional to 1,509.57, 2,264.11 and 413.68 is: 620.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,509.57 : 2,264.11 = 413.68 : x
  2. Step 2: Convert to fraction form
    1,509.57/2,264.11 = 413.68/x
  3. Step 3: Cross multiply
    1,509.57x = 2,264.11 × 413.68
  4. Step 4: Simplify right side
    1,509.57x = 936,617.02
  5. Step 5: Solve for x
    x = 936,617.02/1,509.57
  6. Step 6: Final answer
    x = 620.45

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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.