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Finding the Third Proportional to 697 and 1,427

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Solution

The third proportional to 697 and 1,427 is: 2,921.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    697 : 1,427 = 1,427 : x
  2. Step 2: Convert to fraction form
    697/1,427 = 1,427/x
  3. Step 3: Cross multiply
    697x = 1,427 × 1,427
  4. Step 4: Simplify right side
    697x = 2,036,329
  5. Step 5: Solve for x
    x = 2,036,329/697
  6. Step 6: Final answer
    x = 2,921.56

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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.