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Finding the Third Proportional to 977 and 2,002

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Solution

The third proportional to 977 and 2,002 is: 4,102.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 2,002 = 2,002 : x
  2. Step 2: Convert to fraction form
    977/2,002 = 2,002/x
  3. Step 3: Cross multiply
    977x = 2,002 × 2,002
  4. Step 4: Simplify right side
    977x = 4,008,004
  5. Step 5: Solve for x
    x = 4,008,004/977
  6. Step 6: Final answer
    x = 4,102.36

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.