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Finding the Third Proportional to 5,198 and 5,846

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Solution

The third proportional to 5,198 and 5,846 is: 6,574.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,198 : 5,846 = 5,846 : x
  2. Step 2: Convert to fraction form
    5,198/5,846 = 5,846/x
  3. Step 3: Cross multiply
    5,198x = 5,846 × 5,846
  4. Step 4: Simplify right side
    5,198x = 34,175,716
  5. Step 5: Solve for x
    x = 34,175,716/5,198
  6. Step 6: Final answer
    x = 6,574.78

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.