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Finding the Third Proportional to 1,982 and 4,096

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Solution

The third proportional to 1,982 and 4,096 is: 8,464.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,982 : 4,096 = 4,096 : x
  2. Step 2: Convert to fraction form
    1,982/4,096 = 4,096/x
  3. Step 3: Cross multiply
    1,982x = 4,096 × 4,096
  4. Step 4: Simplify right side
    1,982x = 16,777,216
  5. Step 5: Solve for x
    x = 16,777,216/1,982
  6. Step 6: Final answer
    x = 8,464.79

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.