SOLUTION: Zelma is 18 years older than her son. She was 3 times as old as he was 1 year ago. How old are they now?

Question 248531: Zelma is 18 years older than her son. She was 3 times as old as he was
1 year ago. How old are they now?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Zelda is 18 years older than her son.
Z = S + 18
.
A year ago, she was 3 times her son's age.
We have to say Z-1 and S-1 to represent their ages 1 year ago.
Z-1 = 3*(S-1)
Z-1 = 3S -3
Z = 3S -2
.
We now have Z defined by two equations.
.
S+18 = 3S-2
.
Subtract S from both S
18 = 2S-2
.
Add 2 to both sides
20 = 2S
2S = 20
.
Divide both sides by 2
S = 10, so the son is 10 years old.
.
Looking back at the setup equations.
Z = S + 18
Z = 10 + 18 = 28, so Zelda is 28.
.
How old were they last year?
S = 10-1 = 9
Z = 28-1 = 27
.
To check, was Zelda 3 times as old as her son a year ago?
3*9 = 27
Yes, she was.
.
Done.
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