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Finding the Third Proportional to 6,185 and 7,837

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Solution

The third proportional to 6,185 and 7,837 is: 9,930.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,185 : 7,837 = 7,837 : x
  2. Step 2: Convert to fraction form
    6,185/7,837 = 7,837/x
  3. Step 3: Cross multiply
    6,185x = 7,837 × 7,837
  4. Step 4: Simplify right side
    6,185x = 61,418,569
  5. Step 5: Solve for x
    x = 61,418,569/6,185
  6. Step 6: Final answer
    x = 9,930.25

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.