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Finding the Third Proportional to 4,211 and 9,965

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Solution

The third proportional to 4,211 and 9,965 is: 23,581.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,211 : 9,965 = 9,965 : x
  2. Step 2: Convert to fraction form
    4,211/9,965 = 9,965/x
  3. Step 3: Cross multiply
    4,211x = 9,965 × 9,965
  4. Step 4: Simplify right side
    4,211x = 99,301,225
  5. Step 5: Solve for x
    x = 99,301,225/4,211
  6. Step 6: Final answer
    x = 23,581.39

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.