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Finding the Third Proportional to 299 and 413.50

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Solution

The third proportional to 299 and 413.50 is: 571.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    299 : 413.50 = 413.50 : x
  2. Step 2: Convert to fraction form
    299/413.50 = 413.50/x
  3. Step 3: Cross multiply
    299x = 413.50 × 413.50
  4. Step 4: Simplify right side
    299x = 170,982.25
  5. Step 5: Solve for x
    x = 170,982.25/299
  6. Step 6: Final answer
    x = 571.85

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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.