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Finding the Third Proportional to 82,198 and 123,297

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Solution

The third proportional to 82,198 and 123,297 is: 184,945.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,198 : 123,297 = 123,297 : x
  2. Step 2: Convert to fraction form
    82,198/123,297 = 123,297/x
  3. Step 3: Cross multiply
    82,198x = 123,297 × 123,297
  4. Step 4: Simplify right side
    82,198x = 15,202,150,209
  5. Step 5: Solve for x
    x = 15,202,150,209/82,198
  6. Step 6: Final answer
    x = 184,945.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.