Add some unknown number x years to both ages. Erica will be 8+x years old. Mom will be 42 + x. The goal is to find x so that 3(8+x) = 42 + x - mom is three times as old.
3(8+x) = 42 + x
24 + 3x = 42 + x
2z = 18
x=9
In 9 years Erica will be 17 and mom will be 51. 3 x 17 = 51