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Finding the Third Proportional to 2,538 and 5,214

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Solution

The third proportional to 2,538 and 5,214 is: 10,711.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,538 : 5,214 = 5,214 : x
  2. Step 2: Convert to fraction form
    2,538/5,214 = 5,214/x
  3. Step 3: Cross multiply
    2,538x = 5,214 × 5,214
  4. Step 4: Simplify right side
    2,538x = 27,185,796
  5. Step 5: Solve for x
    x = 27,185,796/2,538
  6. Step 6: Final answer
    x = 10,711.50

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.