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Finding the Third Proportional to 9,823 and 21,203

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Solution

The third proportional to 9,823 and 21,203 is: 45,766.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,823 : 21,203 = 21,203 : x
  2. Step 2: Convert to fraction form
    9,823/21,203 = 21,203/x
  3. Step 3: Cross multiply
    9,823x = 21,203 × 21,203
  4. Step 4: Simplify right side
    9,823x = 449,567,209
  5. Step 5: Solve for x
    x = 449,567,209/9,823
  6. Step 6: Final answer
    x = 45,766.79

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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.