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Finding the Third Proportional to 37,977 and 83,102

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Solution

The third proportional to 37,977 and 83,102 is: 181,845.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,977 : 83,102 = 83,102 : x
  2. Step 2: Convert to fraction form
    37,977/83,102 = 83,102/x
  3. Step 3: Cross multiply
    37,977x = 83,102 × 83,102
  4. Step 4: Simplify right side
    37,977x = 6,905,942,404
  5. Step 5: Solve for x
    x = 6,905,942,404/37,977
  6. Step 6: Final answer
    x = 181,845.39

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.