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Finding the Third Proportional to 83,098 and 180,289

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Solution

The third proportional to 83,098 and 180,289 is: 391,154.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,098 : 180,289 = 180,289 : x
  2. Step 2: Convert to fraction form
    83,098/180,289 = 180,289/x
  3. Step 3: Cross multiply
    83,098x = 180,289 × 180,289
  4. Step 4: Simplify right side
    83,098x = 32,504,123,521
  5. Step 5: Solve for x
    x = 32,504,123,521/83,098
  6. Step 6: Final answer
    x = 391,154.10

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.