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Finding the Third Proportional to 827 and 1,785

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Solution

The third proportional to 827 and 1,785 is: 3,852.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    827 : 1,785 = 1,785 : x
  2. Step 2: Convert to fraction form
    827/1,785 = 1,785/x
  3. Step 3: Cross multiply
    827x = 1,785 × 1,785
  4. Step 4: Simplify right side
    827x = 3,186,225
  5. Step 5: Solve for x
    x = 3,186,225/827
  6. Step 6: Final answer
    x = 3,852.75

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.