Let Dawn's age be x
Kathy's age be x + 15
The sum of their ages= 41
x + (x+15) = 41
2x + 15 = 41
2x + 15 - 15 = 41 - 15
2x = 26
2x/2 = 26/2
x = 13
Their ages:
Dawn: x = 13 years old
Kathy x + 15 = (13) + 15 = 28 years old
To check the sum of their ages:
13 + 28 = 41
41 = 41