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Finding the Third Proportional to 13,223 and 19,837

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Solution

The third proportional to 13,223 and 19,837 is: 29,759.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,223 : 19,837 = 19,837 : x
  2. Step 2: Convert to fraction form
    13,223/19,837 = 19,837/x
  3. Step 3: Cross multiply
    13,223x = 19,837 × 19,837
  4. Step 4: Simplify right side
    13,223x = 393,506,569
  5. Step 5: Solve for x
    x = 393,506,569/13,223
  6. Step 6: Final answer
    x = 29,759.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.