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Finding the Third Proportional to 12,823 and 19,406

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Solution

The third proportional to 12,823 and 19,406 is: 29,368.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,823 : 19,406 = 19,406 : x
  2. Step 2: Convert to fraction form
    12,823/19,406 = 19,406/x
  3. Step 3: Cross multiply
    12,823x = 19,406 × 19,406
  4. Step 4: Simplify right side
    12,823x = 376,592,836
  5. Step 5: Solve for x
    x = 376,592,836/12,823
  6. Step 6: Final answer
    x = 29,368.54

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.