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Finding the Third Proportional to 6,500 and 16,412

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Solution

The third proportional to 6,500 and 16,412 is: 41,439.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 16,412 = 16,412 : x
  2. Step 2: Convert to fraction form
    6,500/16,412 = 16,412/x
  3. Step 3: Cross multiply
    6,500x = 16,412 × 16,412
  4. Step 4: Simplify right side
    6,500x = 269,353,744
  5. Step 5: Solve for x
    x = 269,353,744/6,500
  6. Step 6: Final answer
    x = 41,439.04

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Why These Related Problems?

These problems maintain the same ratio (2.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.