Multiple choice

The average of two numbers is 10 and the product of two numbers is 96. Find the two numbers?

  1. $3, 32$
  2. $12, 8$
  3. $1, 96$
  4. $24, 4$
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B Correct answer
Explanation

Let the numbers be x and y. If average is 10, then (x+y)/2 = 10, so x+y = 20. If product is 96, then xy = 96. Substituting y = 20-x into xy = 96 gives x(20-x) = 96, so -x² + 20x - 96 = 0, or x² - 20x + 96 = 0. Solving: (x-8)(x-12) = 0, so numbers are 8 and 12. This can also be found by checking factor pairs of 96 that sum to 20.

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