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Finding the Third Proportional to 6,401 and 14,038

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Solution

The third proportional to 6,401 and 14,038 is: 30,786.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,401 : 14,038 = 14,038 : x
  2. Step 2: Convert to fraction form
    6,401/14,038 = 14,038/x
  3. Step 3: Cross multiply
    6,401x = 14,038 × 14,038
  4. Step 4: Simplify right side
    6,401x = 197,065,444
  5. Step 5: Solve for x
    x = 197,065,444/6,401
  6. Step 6: Final answer
    x = 30,786.67

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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.