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Finding the Third Proportional to 212,096 and 457,401

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Solution

The third proportional to 212,096 and 457,401 is: 986,419.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,096 : 457,401 = 457,401 : x
  2. Step 2: Convert to fraction form
    212,096/457,401 = 457,401/x
  3. Step 3: Cross multiply
    212,096x = 457,401 × 457,401
  4. Step 4: Simplify right side
    212,096x = 209,215,674,801
  5. Step 5: Solve for x
    x = 209,215,674,801/212,096
  6. Step 6: Final answer
    x = 986,419.71

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.