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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

Answer :

Ryan2
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
AL2006
Labels:
-- 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

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