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Finding the Third Proportional to 742 and 1,233

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Solution

The third proportional to 742 and 1,233 is: 2,048.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    742 : 1,233 = 1,233 : x
  2. Step 2: Convert to fraction form
    742/1,233 = 1,233/x
  3. Step 3: Cross multiply
    742x = 1,233 × 1,233
  4. Step 4: Simplify right side
    742x = 1,520,289
  5. Step 5: Solve for x
    x = 1,520,289/742
  6. Step 6: Final answer
    x = 2,048.91

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.