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Finding the Third Proportional to 1,024 and 2,064

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Solution

The third proportional to 1,024 and 2,064 is: 4,160.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,024 : 2,064 = 2,064 : x
  2. Step 2: Convert to fraction form
    1,024/2,064 = 2,064/x
  3. Step 3: Cross multiply
    1,024x = 2,064 × 2,064
  4. Step 4: Simplify right side
    1,024x = 4,260,096
  5. Step 5: Solve for x
    x = 4,260,096/1,024
  6. Step 6: Final answer
    x = 4,160.25

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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.