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Finding the Third Proportional to 2,198 and 3,583

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Solution

The third proportional to 2,198 and 3,583 is: 5,840.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,198 : 3,583 = 3,583 : x
  2. Step 2: Convert to fraction form
    2,198/3,583 = 3,583/x
  3. Step 3: Cross multiply
    2,198x = 3,583 × 3,583
  4. Step 4: Simplify right side
    2,198x = 12,837,889
  5. Step 5: Solve for x
    x = 12,837,889/2,198
  6. Step 6: Final answer
    x = 5,840.71

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.