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Finding the Third Proportional to 6,500 and 14,234

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Solution

The third proportional to 6,500 and 14,234 is: 31,170.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 14,234 = 14,234 : x
  2. Step 2: Convert to fraction form
    6,500/14,234 = 14,234/x
  3. Step 3: Cross multiply
    6,500x = 14,234 × 14,234
  4. Step 4: Simplify right side
    6,500x = 202,606,756
  5. Step 5: Solve for x
    x = 202,606,756/6,500
  6. Step 6: Final answer
    x = 31,170.27

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.