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Question: 1 / 400

If the sum of two numbers is 20 and their product is 96, what are the two numbers?

12 and 8

To find two numbers where the sum is 20 and the product is 96, we can use a systematic approach involving equations or factoring.

Given that the sum of the two numbers is \(x + y = 20\) and their product is \(xy = 96\), we can express one number in terms of the other. Rearranging the sum equation gives us \(y = 20 - x\). Substituting this expression into the product equation results in \(x(20 - x) = 96\), which simplifies to the quadratic equation \(x^2 - 20x + 96 = 0\).

Factoring the quadratic leads us to find two numbers that not only add up to 20 but also multiply to 96. In this case, the correct factors of the quadratic are derived to be \( (x - 12)(x - 8) = 0\), indicating the solutions \(x = 12\) and \(x = 8\).

Now, examining why the identified numbers satisfy both conditions:

Their sum is indeed \(12 + 8 = 20\) as required. Additionally, their product is \(12 \times 8 = 96\),

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14 and 6

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