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Finding the Third Proportional to 4,000 and 6,412

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Solution

The third proportional to 4,000 and 6,412 is: 10,278.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,000 : 6,412 = 6,412 : x
  2. Step 2: Convert to fraction form
    4,000/6,412 = 6,412/x
  3. Step 3: Cross multiply
    4,000x = 6,412 × 6,412
  4. Step 4: Simplify right side
    4,000x = 41,113,744
  5. Step 5: Solve for x
    x = 41,113,744/4,000
  6. Step 6: Final answer
    x = 10,278.44

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.