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Finding the Third Proportional to 1,538 and 2,005

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Solution

The third proportional to 1,538 and 2,005 is: 2,613.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,538 : 2,005 = 2,005 : x
  2. Step 2: Convert to fraction form
    1,538/2,005 = 2,005/x
  3. Step 3: Cross multiply
    1,538x = 2,005 × 2,005
  4. Step 4: Simplify right side
    1,538x = 4,020,025
  5. Step 5: Solve for x
    x = 4,020,025/1,538
  6. Step 6: Final answer
    x = 2,613.80

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.