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Finding the Third Proportional to 97,648 and 213,991

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Solution

The third proportional to 97,648 and 213,991 is: 468,951.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,648 : 213,991 = 213,991 : x
  2. Step 2: Convert to fraction form
    97,648/213,991 = 213,991/x
  3. Step 3: Cross multiply
    97,648x = 213,991 × 213,991
  4. Step 4: Simplify right side
    97,648x = 45,792,148,081
  5. Step 5: Solve for x
    x = 45,792,148,081/97,648
  6. Step 6: Final answer
    x = 468,951.21

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.