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Finding the Third Proportional to 1,601 and 3,214

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Solution

The third proportional to 1,601 and 3,214 is: 6,452.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,601 : 3,214 = 3,214 : x
  2. Step 2: Convert to fraction form
    1,601/3,214 = 3,214/x
  3. Step 3: Cross multiply
    1,601x = 3,214 × 3,214
  4. Step 4: Simplify right side
    1,601x = 10,329,796
  5. Step 5: Solve for x
    x = 10,329,796/1,601
  6. Step 6: Final answer
    x = 6,452.09

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.