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Finding the Third Proportional to 742 and 1,267

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Solution

The third proportional to 742 and 1,267 is: 2,163.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    742 : 1,267 = 1,267 : x
  2. Step 2: Convert to fraction form
    742/1,267 = 1,267/x
  3. Step 3: Cross multiply
    742x = 1,267 × 1,267
  4. Step 4: Simplify right side
    742x = 1,605,289
  5. Step 5: Solve for x
    x = 1,605,289/742
  6. Step 6: Final answer
    x = 2,163.46

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.