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Finding the Third Proportional to 1,198 and 1,827

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Solution

The third proportional to 1,198 and 1,827 is: 2,786.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,198 : 1,827 = 1,827 : x
  2. Step 2: Convert to fraction form
    1,198/1,827 = 1,827/x
  3. Step 3: Cross multiply
    1,198x = 1,827 × 1,827
  4. Step 4: Simplify right side
    1,198x = 3,337,929
  5. Step 5: Solve for x
    x = 3,337,929/1,198
  6. Step 6: Final answer
    x = 2,786.25

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.