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Finding the Third Proportional to 4,198 and 6,454

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Solution

The third proportional to 4,198 and 6,454 is: 9,922.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,198 : 6,454 = 6,454 : x
  2. Step 2: Convert to fraction form
    4,198/6,454 = 6,454/x
  3. Step 3: Cross multiply
    4,198x = 6,454 × 6,454
  4. Step 4: Simplify right side
    4,198x = 41,654,116
  5. Step 5: Solve for x
    x = 41,654,116/4,198
  6. Step 6: Final answer
    x = 9,922.37

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.