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Finding the Third Proportional to 82,099 and 122,965

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Solution

The third proportional to 82,099 and 122,965 is: 184,172.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,099 : 122,965 = 122,965 : x
  2. Step 2: Convert to fraction form
    82,099/122,965 = 122,965/x
  3. Step 3: Cross multiply
    82,099x = 122,965 × 122,965
  4. Step 4: Simplify right side
    82,099x = 15,120,391,225
  5. Step 5: Solve for x
    x = 15,120,391,225/82,099
  6. Step 6: Final answer
    x = 184,172.66

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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.