Question 419510
Let r = Ruth's age today
Let s = Son's age today

Since Ruth is 22 years older than her son, r = s + 22.
Seven years ago, when Ruth was r - 7 and her son was s - 7, Ruth was 3 time older than her son which means that r - 7 = 3(s - 7)  So we have simultaneous equations:

r = s + 22
r - 7 = 3(s - 7)

Substituting the value of r from the first equation into the second equations, we have:

(s + 22) - 7 = 3(s - 7)
s + 15 = 3s - 21
15 = 2s - 21
36 = 2s
18 = s  the son's age
r = s + 22 = 18 + 22 = 40 which is Ruth's age.

Today, Ruth is 40 and her son is 18.