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Finding the Third Proportional to 12,997 and 19,409

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Solution

The third proportional to 12,997 and 19,409 is: 28,984.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,997 : 19,409 = 19,409 : x
  2. Step 2: Convert to fraction form
    12,997/19,409 = 19,409/x
  3. Step 3: Cross multiply
    12,997x = 19,409 × 19,409
  4. Step 4: Simplify right side
    12,997x = 376,709,281
  5. Step 5: Solve for x
    x = 376,709,281/12,997
  6. Step 6: Final answer
    x = 28,984.33

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.