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Finding the Third Proportional to 82,278 and 194,031

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Solution

The third proportional to 82,278 and 194,031 is: 457,571.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,278 : 194,031 = 194,031 : x
  2. Step 2: Convert to fraction form
    82,278/194,031 = 194,031/x
  3. Step 3: Cross multiply
    82,278x = 194,031 × 194,031
  4. Step 4: Simplify right side
    82,278x = 37,648,028,961
  5. Step 5: Solve for x
    x = 37,648,028,961/82,278
  6. Step 6: Final answer
    x = 457,571.03

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.