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Finding the Third Proportional to 2,198 and 4,284

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Solution

The third proportional to 2,198 and 4,284 is: 8,349.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,198 : 4,284 = 4,284 : x
  2. Step 2: Convert to fraction form
    2,198/4,284 = 4,284/x
  3. Step 3: Cross multiply
    2,198x = 4,284 × 4,284
  4. Step 4: Simplify right side
    2,198x = 18,352,656
  5. Step 5: Solve for x
    x = 18,352,656/2,198
  6. Step 6: Final answer
    x = 8,349.71

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.