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Finding the Third Proportional to 3,299 and 7,697

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Solution

The third proportional to 3,299 and 7,697 is: 17,958.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,299 : 7,697 = 7,697 : x
  2. Step 2: Convert to fraction form
    3,299/7,697 = 7,697/x
  3. Step 3: Cross multiply
    3,299x = 7,697 × 7,697
  4. Step 4: Simplify right side
    3,299x = 59,243,809
  5. Step 5: Solve for x
    x = 59,243,809/3,299
  6. Step 6: Final answer
    x = 17,958.11

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.