Multiple choice

The average of two numbers is $6$ and four times the difference between then is $16$. Find the numbers.

  1. $5$ & $10$
  2. $8$ & $4$
  3. $8$ & $14$
  4. $2$ & $8$
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B Correct answer
Explanation

Let numbers be x and y. (x+y)/2 = 6 => x+y = 12. 4|x-y| = 16 => |x-y| = 4. Solving x+y=12 and x-y=4 gives x=8, y=4.

AI explanation

By the definition of an average, the sum of the two numbers is 2 times 6, which equals 12. The difference between the two numbers is 16 divided by 4, giving 4. Letting the numbers be x and y creates the system x plus y equals 12 and x minus y equals 4; adding the equations gives 2x equals 16, so x is 8. Substituting 8 into the first equation gives y equals 4, making the numbers 8 and 4.

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