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Finding the Third Proportional to 106,414 and 222,683

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Solution

The third proportional to 106,414 and 222,683 is: 465,988.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,414 : 222,683 = 222,683 : x
  2. Step 2: Convert to fraction form
    106,414/222,683 = 222,683/x
  3. Step 3: Cross multiply
    106,414x = 222,683 × 222,683
  4. Step 4: Simplify right side
    106,414x = 49,587,718,489
  5. Step 5: Solve for x
    x = 49,587,718,489/106,414
  6. Step 6: Final answer
    x = 465,988.67

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.