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Finding the Third Proportional to 820 and 1,286

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Solution

The third proportional to 820 and 1,286 is: 2,016.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    820 : 1,286 = 1,286 : x
  2. Step 2: Convert to fraction form
    820/1,286 = 1,286/x
  3. Step 3: Cross multiply
    820x = 1,286 × 1,286
  4. Step 4: Simplify right side
    820x = 1,653,796
  5. Step 5: Solve for x
    x = 1,653,796/820
  6. Step 6: Final answer
    x = 2,016.82

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.