SOLUTION: ruth is 22 years older than her son. 7 years ago ruth was 3 times her sons age... how old are they now?

Question 419510: ruth is 22 years older than her son. 7 years ago ruth was 3 times her sons age... how old are they now?
Answer by duckness73(47) (Show Source): You can put this solution on YOUR website!
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.
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