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Finding the Fourth Proportional to 1,509.57, 2,264.31 and 413.93

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Solution

The fourth proportional to 1,509.57, 2,264.31 and 413.93 is: 620.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,509.57 : 2,264.31 = 413.93 : x
  2. Step 2: Convert to fraction form
    1,509.57/2,264.31 = 413.93/x
  3. Step 3: Cross multiply
    1,509.57x = 2,264.31 × 413.93
  4. Step 4: Simplify right side
    1,509.57x = 937,271.50
  5. Step 5: Solve for x
    x = 937,271.50/1,509.57
  6. Step 6: Final answer
    x = 620.89

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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.