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Finding the Third Proportional to 13,096 and 19,581

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Solution

The third proportional to 13,096 and 19,581 is: 29,277.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,096 : 19,581 = 19,581 : x
  2. Step 2: Convert to fraction form
    13,096/19,581 = 19,581/x
  3. Step 3: Cross multiply
    13,096x = 19,581 × 19,581
  4. Step 4: Simplify right side
    13,096x = 383,415,561
  5. Step 5: Solve for x
    x = 383,415,561/13,096
  6. Step 6: Final answer
    x = 29,277.30

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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.