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Finding the Third Proportional to 2,978 and 6,538

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Solution

The third proportional to 2,978 and 6,538 is: 14,353.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,978 : 6,538 = 6,538 : x
  2. Step 2: Convert to fraction form
    2,978/6,538 = 6,538/x
  3. Step 3: Cross multiply
    2,978x = 6,538 × 6,538
  4. Step 4: Simplify right side
    2,978x = 42,745,444
  5. Step 5: Solve for x
    x = 42,745,444/2,978
  6. Step 6: Final answer
    x = 14,353.74

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.