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Finding the Third Proportional to 294.94 and 413.72

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Solution

The third proportional to 294.94 and 413.72 is: 580.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    294.94 : 413.72 = 413.72 : x
  2. Step 2: Convert to fraction form
    294.94/413.72 = 413.72/x
  3. Step 3: Cross multiply
    294.94x = 413.72 × 413.72
  4. Step 4: Simplify right side
    294.94x = 171,163.20
  5. Step 5: Solve for x
    x = 171,163.20/294.94
  6. Step 6: Final answer
    x = 580.34

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.