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Finding the Third Proportional to 271,986 and 408,216

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Solution

The third proportional to 271,986 and 408,216 is: 612,679.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    271,986 : 408,216 = 408,216 : x
  2. Step 2: Convert to fraction form
    271,986/408,216 = 408,216/x
  3. Step 3: Cross multiply
    271,986x = 408,216 × 408,216
  4. Step 4: Simplify right side
    271,986x = 166,640,302,656
  5. Step 5: Solve for x
    x = 166,640,302,656/271,986
  6. Step 6: Final answer
    x = 612,679.71

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.