Multiple choice

If the average of 5 and x is equal to the average of 2, 6 and x, what is the value of x?

  1. 1

  2. 2

  3. 5

  4. 6

  5. 8
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A Correct answer
Explanation

The average of 5 and x is (5+x)/2. The average of 2, 6, and x is (2+6+x)/3 = (8+x)/3. Setting them equal: (5+x)/2 = (8+x)/3. Cross-multiplying gives 3(5+x) = 2(8+x), so 15 + 3x = 16 + 2x, which leads to x = 1.

AI explanation

The formula for an average is the sum of the terms divided by the number of terms. Setting the two averages equal gives the equation (5 + x) / 2 = (2 + 6 + x) / 3. Cross-multiplying yields 3 times (5 + x) = 2 times (8 + x), which simplifies to 15 + 3x = 16 + 2x. Solving for x by subtracting 2x and 15 from both sides gives x = 1. The result is 1.

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