Answer:
Kathy is 48 years old and Samantha is 12.
Explanation:
This is a challenging question that requires some interpretation. Let K and S stand for the current ages of Kathy and Samatha.
We are told that: K+S = 60
And, in 8 years: K+8 and S+8
"Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago" ["3 years ago:" from now or in 8 years. I'll interpret it as from now, or (S-3)]
(K+8) = 3(S+8-3)+5 ["5 years older than 3 times as old as Samantha was 3 years ago"]
(K+8) = 3(S+5)+5
K+8 = 3S+20
K = 3S+12
---
Rearrange the firts equation to isolate K
K = 60-S
Now use this definition of K in the previous equation:
K = 3S+12
60-S = 3S+12
4S = 48
S = 12
K+S = 60
K+12 = 60
K = 48
=====
CHECK
Does K + S = 60? 48+12 = 60 YES
In 8 years, will Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago?
K = 48+8 = 56
S = 12+8 = 20
Three years ago S was 9.
(K+8) = 3(S+8-3)+5
(K+8) = 3(12+8-3)+5
K + 8 = 3(17)+5
K = 48
===
Kathy is 48 years old and Samantha is 12.