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Finding the Third Proportional to 12,106 and 19,023

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Solution

The third proportional to 12,106 and 19,023 is: 29,892.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,106 : 19,023 = 19,023 : x
  2. Step 2: Convert to fraction form
    12,106/19,023 = 19,023/x
  3. Step 3: Cross multiply
    12,106x = 19,023 × 19,023
  4. Step 4: Simplify right side
    12,106x = 361,874,529
  5. Step 5: Solve for x
    x = 361,874,529/12,106
  6. Step 6: Final answer
    x = 29,892.16

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.