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Finding the Fourth Proportional to 1,024, 1,413.84 and 712.96

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Solution

The fourth proportional to 1,024, 1,413.84 and 712.96 is: 984.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,024 : 1,413.84 = 712.96 : x
  2. Step 2: Convert to fraction form
    1,024/1,413.84 = 712.96/x
  3. Step 3: Cross multiply
    1,024x = 1,413.84 × 712.96
  4. Step 4: Simplify right side
    1,024x = 1,008,011.37
  5. Step 5: Solve for x
    x = 1,008,011.37/1,024
  6. Step 6: Final answer
    x = 984.39

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.