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Finding the Third Proportional to 213 and 413.50

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Solution

The third proportional to 213 and 413.50 is: 802.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 413.50 = 413.50 : x
  2. Step 2: Convert to fraction form
    213/413.50 = 413.50/x
  3. Step 3: Cross multiply
    213x = 413.50 × 413.50
  4. Step 4: Simplify right side
    213x = 170,982.25
  5. Step 5: Solve for x
    x = 170,982.25/213
  6. Step 6: Final answer
    x = 802.73

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.