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Finding the Third Proportional to 82,411 and 177,962

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Solution

The third proportional to 82,411 and 177,962 is: 384,299.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,411 : 177,962 = 177,962 : x
  2. Step 2: Convert to fraction form
    82,411/177,962 = 177,962/x
  3. Step 3: Cross multiply
    82,411x = 177,962 × 177,962
  4. Step 4: Simplify right side
    82,411x = 31,670,473,444
  5. Step 5: Solve for x
    x = 31,670,473,444/82,411
  6. Step 6: Final answer
    x = 384,299.10

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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.