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Finding the Third Proportional to 82,296 and 177,408

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Solution

The third proportional to 82,296 and 177,408 is: 382,443.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,296 : 177,408 = 177,408 : x
  2. Step 2: Convert to fraction form
    82,296/177,408 = 177,408/x
  3. Step 3: Cross multiply
    82,296x = 177,408 × 177,408
  4. Step 4: Simplify right side
    82,296x = 31,473,598,464
  5. Step 5: Solve for x
    x = 31,473,598,464/82,296
  6. Step 6: Final answer
    x = 382,443.84

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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.