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Finding the Third Proportional to 82,541 and 180,857

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Solution

The third proportional to 82,541 and 180,857 is: 396,278.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,541 : 180,857 = 180,857 : x
  2. Step 2: Convert to fraction form
    82,541/180,857 = 180,857/x
  3. Step 3: Cross multiply
    82,541x = 180,857 × 180,857
  4. Step 4: Simplify right side
    82,541x = 32,709,254,449
  5. Step 5: Solve for x
    x = 32,709,254,449/82,541
  6. Step 6: Final answer
    x = 396,278.87

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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.