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Finding the Third Proportional to 1,024 and 2,782

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Solution

The third proportional to 1,024 and 2,782 is: 7,558.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,024 : 2,782 = 2,782 : x
  2. Step 2: Convert to fraction form
    1,024/2,782 = 2,782/x
  3. Step 3: Cross multiply
    1,024x = 2,782 × 2,782
  4. Step 4: Simplify right side
    1,024x = 7,739,524
  5. Step 5: Solve for x
    x = 7,739,524/1,024
  6. Step 6: Final answer
    x = 7,558.13

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Why These Related Problems?

These problems maintain the same ratio (2.72) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.