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How old is each girl?

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2 Answers

Let's assume that Jane is (x) years old, then Lina will be (x + 5) years old.

Eight years ago Jane was [(x) - 8] years old. Lina was [(x + 5) - 8] years old.

(x + 5) - 8 = 3*(x - 8)
x - 3 = 3x - 24
2x = 21
x = 10.5

Jane is 10.5 years old, and Lina is 15.5 years old

(Just for check: Eight years ago Jane was 2.5 y. o., and Lina was 7.5 y. o.)
Hi Rose;
Lina is 5 years older than Jane. Eight years ago she was three times the age of Jane.
 
x=Jane's age
x+5=Lina's age
 
Eight years ago...
x-8=Jane's age
x+5-8=Lina's age
 
3(x-8)=(x-3)
3x-24=x-3
Let's isolate x...
Let's add 3 to both sides...
3x-24+3=x-3+3
3x-21=x
Let's subtract 3x from both sides...
-3x+3x-21=x-3x
-21=-2x
Let's divide both sides by -2...
-21/-2=-2x/-2
10.5=x
 
10.5=Jane's age
15.5=Lina's age
 
Eight years ago...
2.5=Jane's age
7.5=Lina's age
 
(3)(2.5)=7.5