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Finding the Third Proportional to 4,198 and 7,769

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Solution

The third proportional to 4,198 and 7,769 is: 14,377.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,198 : 7,769 = 7,769 : x
  2. Step 2: Convert to fraction form
    4,198/7,769 = 7,769/x
  3. Step 3: Cross multiply
    4,198x = 7,769 × 7,769
  4. Step 4: Simplify right side
    4,198x = 60,357,361
  5. Step 5: Solve for x
    x = 60,357,361/4,198
  6. Step 6: Final answer
    x = 14,377.65

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.