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

Sove the system:x: Mary´s agey: Mom´s age:x + y = 673x + 7 = yReplace y in the first equation:x + 3x + 7 = 674x = 67 - 74x = 60x = 15 yrs.y = 67  - 15 = 52 yrs

Labels:-- Mary's age = D (for 'daughter')-- Mom's age = M (for 'mom')The problem says 2 things:         D + M = 67and       3D + 7 = M .Let's subtract 'M' from each side of the first one:  D = 67 - MNow 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 = MAdd 3m to each side:       201        + 7 = 4M       208              = 4MDivide each side by 4 :       52 = Mom's ageDaughter's age = 67 - Mom's age = 67 - 52 = 15