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Finding the Third Proportional to 9,677 and 21,199

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Solution

The third proportional to 9,677 and 21,199 is: 46,439.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,677 : 21,199 = 21,199 : x
  2. Step 2: Convert to fraction form
    9,677/21,199 = 21,199/x
  3. Step 3: Cross multiply
    9,677x = 21,199 × 21,199
  4. Step 4: Simplify right side
    9,677x = 449,397,601
  5. Step 5: Solve for x
    x = 449,397,601/9,677
  6. Step 6: Final answer
    x = 46,439.76

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.