♥ I need help with an algebraic birthday problem.. Any math geniuses???

Question

okay, here's the problem. "Tina and Louise both celebrate their birthdays today. In 3 years Tina will be four times as old as Louise was when Tina was 2 years older than Louise is today. If Louise is a teenager, what is Tina's age?"
So if anyone can help me with this problem I'm willing to give away extra points to on other questions.
Please help me!!

Answer 1

Let T and L be their current ages. The difference in their ages is T - L.

In 3 years, their ages will be T+3 and L+3

When Tina was L+2, Louise was L+2 - (T-L) = 2L-T+2

So T+3 = 4*(2L - T + 2)
5T = 8L + 5
Clearly L must be a multiple of 5 so L = 15.
T = 25

Answer 2

T = age Tina today
L = age Louise today

T + 3 = 4{L - (T - (L + 2)]} = 4{L - T + L + 2}
T + 3 = 4(2L - T + 2)
T + 3 = 8L - 4T + 8
5T = 8L + 5
T = (8/5)L + 1

I assume we want integer ages. Since Louise is a teenager then

L = 15

T = (8/5)L + 1 = (8/5)15 + 1 = 24 + 1 = 25

Louise is 15 and Tina is 25.

Answer 3

T+3 = 4((L-n))
L = (T-n) -2
12
n, L, T are all positive integers

L + 2 + n + 3 = 4L - 4n
3L = 5 + 5n
L = (n+1)5/3

n = 7,8,9,10
for n = 7, L = 13.333, T = 22.333
for n = 8, L = 15, T = 25
for n = 9, L = 16.667, T = 27.667
for n = 10, L = 18.333, T = 30.333

L = 15, T = 25 is the only answer that meets all the criteria.

Answer 4

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