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Finding the Third Proportional to 82,671 and 177,006

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Solution

The third proportional to 82,671 and 177,006 is: 378,985.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,671 : 177,006 = 177,006 : x
  2. Step 2: Convert to fraction form
    82,671/177,006 = 177,006/x
  3. Step 3: Cross multiply
    82,671x = 177,006 × 177,006
  4. Step 4: Simplify right side
    82,671x = 31,331,124,036
  5. Step 5: Solve for x
    x = 31,331,124,036/82,671
  6. Step 6: Final answer
    x = 378,985.67

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.