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Finding the Third Proportional to 2,024 and 4,096

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Solution

The third proportional to 2,024 and 4,096 is: 8,289.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,024 : 4,096 = 4,096 : x
  2. Step 2: Convert to fraction form
    2,024/4,096 = 4,096/x
  3. Step 3: Cross multiply
    2,024x = 4,096 × 4,096
  4. Step 4: Simplify right side
    2,024x = 16,777,216
  5. Step 5: Solve for x
    x = 16,777,216/2,024
  6. Step 6: Final answer
    x = 8,289.14

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.