Question

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 1

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

Answer 2

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