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Finding the Third Proportional to 697 and 1,538

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Solution

The third proportional to 697 and 1,538 is: 3,393.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    697 : 1,538 = 1,538 : x
  2. Step 2: Convert to fraction form
    697/1,538 = 1,538/x
  3. Step 3: Cross multiply
    697x = 1,538 × 1,538
  4. Step 4: Simplify right side
    697x = 2,365,444
  5. Step 5: Solve for x
    x = 2,365,444/697
  6. Step 6: Final answer
    x = 3,393.75

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.