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Finding the Third Proportional to 906 and 2,166

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Solution

The third proportional to 906 and 2,166 is: 5,178.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    906 : 2,166 = 2,166 : x
  2. Step 2: Convert to fraction form
    906/2,166 = 2,166/x
  3. Step 3: Cross multiply
    906x = 2,166 × 2,166
  4. Step 4: Simplify right side
    906x = 4,691,556
  5. Step 5: Solve for x
    x = 4,691,556/906
  6. Step 6: Final answer
    x = 5,178.32

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Why These Related Problems?

These problems maintain the same ratio (2.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.