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Finding the Third Proportional to 969 and 1,965

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Solution

The third proportional to 969 and 1,965 is: 3,984.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    969 : 1,965 = 1,965 : x
  2. Step 2: Convert to fraction form
    969/1,965 = 1,965/x
  3. Step 3: Cross multiply
    969x = 1,965 × 1,965
  4. Step 4: Simplify right side
    969x = 3,861,225
  5. Step 5: Solve for x
    x = 3,861,225/969
  6. Step 6: Final answer
    x = 3,984.75

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.