How old is each girl?

Question

Lina is 5 years older than Jane. Eight years ago she was three times the age of Jane.

Answer 1

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.)

Answer 2

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