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Finding the Third Proportional to 1,682 and 1,838

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Solution

The third proportional to 1,682 and 1,838 is: 2,008.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,682 : 1,838 = 1,838 : x
  2. Step 2: Convert to fraction form
    1,682/1,838 = 1,838/x
  3. Step 3: Cross multiply
    1,682x = 1,838 × 1,838
  4. Step 4: Simplify right side
    1,682x = 3,378,244
  5. Step 5: Solve for x
    x = 3,378,244/1,682
  6. Step 6: Final answer
    x = 2,008.47

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.