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27 December, 06:49

The sum of two numbers is 38. The greater number is 8 more than the other number. Find each number. Use a system of linear equations to justify your answer

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Answers (1)
  1. 27 December, 07:08
    0
    The smaller number is

    3

    (The other number is therefore

    5

    )

    Explanation:

    We could use

    x

    and

    y

    to represent the two numbers, but it is possible to form an equation using only one variable.

    If two numbers add up to 8, and we let one of them be

    x

    , the other one will be the difference, which is:

    8

    -

    x

    The sum of their squares is

    34

    x

    2

    +

    (

    8

    -

    x

    )

    2

    =

    34



    (

    a

    -

    b

    )

    2

    =

    a

    2

    -

    2

    a

    b

    +

    b

    2

    x

    2

    +

    64

    -

    16

    x

    +

    x

    2

    =

    34

    2

    x

    2

    -

    16

    x

    +

    64

    -

    34

    =

    0

    2

    x

    2

    -

    16

    x

    +

    30

    =

    0



    :

    2

    x

    2

    -

    8

    x

    +

    15

    =

    0



    find factors of 15 which add to 8.

    (

    x

    -

    3

    )

    (

    x

    -

    5

    )

    =

    0

    Setting factor equal to

    0

    gives:

    x

    =

    3

    and

    x

    =

    5

    Check:

    3

    +

    5

    =

    8

    3

    2

    +

    5

    2

    =

    9

    +

    25

    =

    34
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