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Finding the Third Proportional to 5,976 and 14,064

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Solution

The third proportional to 5,976 and 14,064 is: 33,098.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,976 : 14,064 = 14,064 : x
  2. Step 2: Convert to fraction form
    5,976/14,064 = 14,064/x
  3. Step 3: Cross multiply
    5,976x = 14,064 × 14,064
  4. Step 4: Simplify right side
    5,976x = 197,796,096
  5. Step 5: Solve for x
    x = 197,796,096/5,976
  6. Step 6: Final answer
    x = 33,098.41

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.