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Finding the Third Proportional to 12,144 and 16,409

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Solution

The third proportional to 12,144 and 16,409 is: 22,171.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,144 : 16,409 = 16,409 : x
  2. Step 2: Convert to fraction form
    12,144/16,409 = 16,409/x
  3. Step 3: Cross multiply
    12,144x = 16,409 × 16,409
  4. Step 4: Simplify right side
    12,144x = 269,255,281
  5. Step 5: Solve for x
    x = 269,255,281/12,144
  6. Step 6: Final answer
    x = 22,171.88

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.