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Finding the Third Proportional to 2,039 and 4,199

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Solution

The third proportional to 2,039 and 4,199 is: 8,647.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,039 : 4,199 = 4,199 : x
  2. Step 2: Convert to fraction form
    2,039/4,199 = 4,199/x
  3. Step 3: Cross multiply
    2,039x = 4,199 × 4,199
  4. Step 4: Simplify right side
    2,039x = 17,631,601
  5. Step 5: Solve for x
    x = 17,631,601/2,039
  6. Step 6: Final answer
    x = 8,647.18

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.