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Finding the Third Proportional to 12,854 and 19,497

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Solution

The third proportional to 12,854 and 19,497 is: 29,573.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,854 : 19,497 = 19,497 : x
  2. Step 2: Convert to fraction form
    12,854/19,497 = 19,497/x
  3. Step 3: Cross multiply
    12,854x = 19,497 × 19,497
  4. Step 4: Simplify right side
    12,854x = 380,133,009
  5. Step 5: Solve for x
    x = 380,133,009/12,854
  6. Step 6: Final answer
    x = 29,573.13

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.