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11 June, 22:36

The sum of Marys age and her moms age is 67. Three times Marys age increased by 7 is her moms age. How old is Mary and her mother

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  1. 11 June, 22:45
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    - - Mary's age = D (for 'daughter')

    - - Mom's age = M (for 'mom')

    The problem says 2 things:

    D + M = 67

    and

    3D + 7 = M.

    Let's subtract 'M' from each side of the first one: D = 67 - M

    Now we can plug that into the second one, in place of 'D'.

    3D + 7 = M

    3 (67 - M) + 7 = M.

    Clear the parentheses on the left side. I assume you know how to do that.

    201 - 3M + 7 = M

    Add 3m to each side:

    201 + 7 = 4M

    208 = 4M

    Divide each side by 4:

    52 = Mom's age

    Daughter's age = 67 - Mom's age = 67 - 52 = 15
  2. 11 June, 23:04
    0
    Sove the system:

    x: Mary's age

    y: Mom's age:

    x + y = 67

    3x + 7 = y

    Replace y in the first equation:

    x + 3x + 7 = 67

    4x = 67 - 7

    4x = 60

    x = 15 yrs.

    y = 67 - 15 = 52 yrs
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