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Finding the Third Proportional to 2,014 and 4,211

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Solution

The third proportional to 2,014 and 4,211 is: 8,804.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,014 : 4,211 = 4,211 : x
  2. Step 2: Convert to fraction form
    2,014/4,211 = 4,211/x
  3. Step 3: Cross multiply
    2,014x = 4,211 × 4,211
  4. Step 4: Simplify right side
    2,014x = 17,732,521
  5. Step 5: Solve for x
    x = 17,732,521/2,014
  6. Step 6: Final answer
    x = 8,804.63

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.