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Finding the Third Proportional to 2,077 and 4,517

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Solution

The third proportional to 2,077 and 4,517 is: 9,823.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,077 : 4,517 = 4,517 : x
  2. Step 2: Convert to fraction form
    2,077/4,517 = 4,517/x
  3. Step 3: Cross multiply
    2,077x = 4,517 × 4,517
  4. Step 4: Simplify right side
    2,077x = 20,403,289
  5. Step 5: Solve for x
    x = 20,403,289/2,077
  6. Step 6: Final answer
    x = 9,823.44

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.