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Finding the Third Proportional to 83,084 and 180,191

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Solution

The third proportional to 83,084 and 180,191 is: 390,794.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,084 : 180,191 = 180,191 : x
  2. Step 2: Convert to fraction form
    83,084/180,191 = 180,191/x
  3. Step 3: Cross multiply
    83,084x = 180,191 × 180,191
  4. Step 4: Simplify right side
    83,084x = 32,468,796,481
  5. Step 5: Solve for x
    x = 32,468,796,481/83,084
  6. Step 6: Final answer
    x = 390,794.82

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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.