Find two numbers whose sum is 47 and whose product is 496. (Enter your answers as a comma-separated list.)

the numbers are 16 and 31

Step-by-step explanation:

Let x represent one of the numbers.

Let y represent the other number.

The sum of the two numbers is 47. This means that

x + y = 47

The product of the numbers is 496. This means that

xy = 496 - - - - - - - - - - - -1

Substituting x = 47 - y into equation 1, it becomes

y(47 - y) = 496

47y - y² = 496

y² - 47y + 496 = 0

y² - 16y - 31y + 496 = 0

y(y - 16) - 31(y - 16) = 0

(y - 31)(y - 16) = 0

y = 31 or y = 16

x = 47 - 16 = 31

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