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21 November, 00:00

Solve the following problem. show all steps (V. E. S. T.) The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.?.

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  1. 21 November, 00:18
    0
    We have three numbers:

    first number=x

    second number=2x

    third number=2x+6

    we can suggest this equation:

    x+2x + (2x+6) = 26

    x+2x+2x=26-6

    5x=20

    x=20/5

    x=4

    First number=x=4

    second number=2x=2 (4) = 8

    third number=2x+6=2 (4) + 6=8+6=14

    Answer: the numbers are 4, 8 and 14.
  2. 21 November, 01:06
    0
    The sum of three numbers is 26."

    x+y+z = 26

    "the second number is twice the first"

    y = 2x

    "the third number is 6 more than the second"

    z = 6+y

    You have the system of equations

    x + y + z = 26

    2x - y = 0

    -y + z = 6

    Solve using Gauss-Jordan Elimination:

    x+y+z = 26

    -3y-2z = - 52

    -y+z = 6

    x+y+z = 26

    y + (2/3) z = 52/3

    -y+z = 6

    x + (1/3) z = 26/3

    y + (2/3) z = 52/3

    (5/3) z = 70/3

    x + (1/3) z = 26/3

    y + (2/3) z = 52/3

    z = 14

    x = 4

    y = 8

    z = 14
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