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Finding the Third Proportional to 82,084 and 180,368

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Solution

The third proportional to 82,084 and 180,368 is: 396,333.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,084 : 180,368 = 180,368 : x
  2. Step 2: Convert to fraction form
    82,084/180,368 = 180,368/x
  3. Step 3: Cross multiply
    82,084x = 180,368 × 180,368
  4. Step 4: Simplify right side
    82,084x = 32,532,615,424
  5. Step 5: Solve for x
    x = 32,532,615,424/82,084
  6. Step 6: Final answer
    x = 396,333.21

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.