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Finding the Third Proportional to 12,384 and 16,176

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Solution

The third proportional to 12,384 and 16,176 is: 21,129.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,384 : 16,176 = 16,176 : x
  2. Step 2: Convert to fraction form
    12,384/16,176 = 16,176/x
  3. Step 3: Cross multiply
    12,384x = 16,176 × 16,176
  4. Step 4: Simplify right side
    12,384x = 261,662,976
  5. Step 5: Solve for x
    x = 261,662,976/12,384
  6. Step 6: Final answer
    x = 21,129.12

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.