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Finding the Third Proportional to 2,538 and 3,815

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Solution

The third proportional to 2,538 and 3,815 is: 5,734.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,538 : 3,815 = 3,815 : x
  2. Step 2: Convert to fraction form
    2,538/3,815 = 3,815/x
  3. Step 3: Cross multiply
    2,538x = 3,815 × 3,815
  4. Step 4: Simplify right side
    2,538x = 14,554,225
  5. Step 5: Solve for x
    x = 14,554,225/2,538
  6. Step 6: Final answer
    x = 5,734.53

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.