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Finding the Third Proportional to 50,414 and 106,024

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Solution

The third proportional to 50,414 and 106,024 is: 222,975.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    50,414 : 106,024 = 106,024 : x
  2. Step 2: Convert to fraction form
    50,414/106,024 = 106,024/x
  3. Step 3: Cross multiply
    50,414x = 106,024 × 106,024
  4. Step 4: Simplify right side
    50,414x = 11,241,088,576
  5. Step 5: Solve for x
    x = 11,241,088,576/50,414
  6. Step 6: Final answer
    x = 222,975.53

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.