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Finding the Third Proportional to 12,096 and 16,576

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Solution

The third proportional to 12,096 and 16,576 is: 22,715.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,096 : 16,576 = 16,576 : x
  2. Step 2: Convert to fraction form
    12,096/16,576 = 16,576/x
  3. Step 3: Cross multiply
    12,096x = 16,576 × 16,576
  4. Step 4: Simplify right side
    12,096x = 274,763,776
  5. Step 5: Solve for x
    x = 274,763,776/12,096
  6. Step 6: Final answer
    x = 22,715.26

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.