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Finding the Third Proportional to 82,019 and 107,697

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Solution

The third proportional to 82,019 and 107,697 is: 141,414.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,019 : 107,697 = 107,697 : x
  2. Step 2: Convert to fraction form
    82,019/107,697 = 107,697/x
  3. Step 3: Cross multiply
    82,019x = 107,697 × 107,697
  4. Step 4: Simplify right side
    82,019x = 11,598,643,809
  5. Step 5: Solve for x
    x = 11,598,643,809/82,019
  6. Step 6: Final answer
    x = 141,414.11

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.