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Finding the Third Proportional to 6,986 and 7,538

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Solution

The third proportional to 6,986 and 7,538 is: 8,133.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,986 : 7,538 = 7,538 : x
  2. Step 2: Convert to fraction form
    6,986/7,538 = 7,538/x
  3. Step 3: Cross multiply
    6,986x = 7,538 × 7,538
  4. Step 4: Simplify right side
    6,986x = 56,821,444
  5. Step 5: Solve for x
    x = 56,821,444/6,986
  6. Step 6: Final answer
    x = 8,133.62

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.