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Finding the Third Proportional to 7,837 and 16,322

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Solution

The third proportional to 7,837 and 16,322 is: 33,993.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,837 : 16,322 = 16,322 : x
  2. Step 2: Convert to fraction form
    7,837/16,322 = 16,322/x
  3. Step 3: Cross multiply
    7,837x = 16,322 × 16,322
  4. Step 4: Simplify right side
    7,837x = 266,407,684
  5. Step 5: Solve for x
    x = 266,407,684/7,837
  6. Step 6: Final answer
    x = 33,993.58

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.