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1 November, 04:56

Product 48 and sum 14 what are the factors

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Answers (2)
  1. 1 November, 06:46
    0
    Step-by-step explanation:

    Let's write a system.

    Let's say that the variables are x and y.

    xy=48

    x+y=14

    Solve for one of the variables, let's say, x.

    x=14-y.

    Now substitute x into the 1st equation.

    (14-y) y=48

    Simplify.

    -y²+14y=48

    Make it into a quadratic equation.

    -y²+14y-48=0

    Make sure y²'s coefficient is one. Divide everything by - 1

    y²-14y+48=0

    Now factor!

    What factors add up to 14 and multiply to 48.

    6 and 8!

    Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.

    y²-6y-8y+48=0

    Group.

    (y²-6y) + (-8y+48) = 0

    y (y-6) - 8 (y-6) = 0

    (y-8) (y-6) = 0

    y-8=0

    y-6=0

    y=8 y=6

    now let's substitute each y value into y²-14y+48=0

    8²-14 (8) + 48=0

    64-112+48=0

    0=0. so y=8 checks out!

    6²-14 (6) + 48=0

    36-84+48=0

    0=0 so y=6 also checks out!

    Choose one y value and solve for x, in each equation:

    xy=48

    x+y=14

    8x=48

    x+8=14

    x=6

    x=6

    It checks out!

    so the factors are

    x=6 y=8.
  2. 1 November, 08:10
    0
    6 and 8

    6*8 = 48

    6+8 = 14
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