Tricky Tricky question

Hello SweatyPerson!

Tina and Louise both celebrate their birthdays today.  In three years, Tina will be four times as old as Louise was when Tina was two years older than Louise is today.  If Louise is a teenager, how old is Tina?

Tina und Louise feiern beide heute ihre Geburtstage. In drei Jahren wird Tina viermal so alt sein, wie Louise war, als Tina zwei Jahre älter war als Louise heute ist. Wenn Louise ein Teenager ist, wie alt ist Tina ?

ℤ(10) = {10...19}

∈ℤ(10) = birthday (age) Louise

x = Years ago the Birthday

∈ℤ(10) - x = Louise x years ago

∈ℤ(10) - x + 2 = Tina x years ago

(∈ℤ(10) - x) * 4 = Tina in 3 years

(∈ℤ(10) - x) * 4 - 3 = Tina today

Tina x years ago + x + 3 = Tina in 3 years

∈ℤ(10) - x + 2 + x + 3 = (∈ℤ(10) - x) * 4

∈ℤ(10) + 5 = 4 * ∈ℤ(10) - 4x

x = (3 * ∈ℤ(10) -  5) / 4

There are three solutions:

∈ℤ(10) =  10    11    12    13    14   15    16       17     18     19

         x =  6.25   7   7.75  8.5  10.5  10  10.75  11.5  12.25  13

x = 7   ∈ℤ(10) = 11

Louise is 11 years old.

(∈ℤ(10) - x) * 4 - 3 = (11 - 7) * 4 - 3 = 13

Tina is 13.

x = 10   ∈ℤ(10) = 15

Louise is 15 years old.

(∈ℤ(10) - x) * 4 - 3 = (15 - 10) * 4 - 3 = 17

Tina is 17.

x = 13   ∈ℤ(10) = 19

Louise is 19 years old.

(∈ℤ(10) - x) * 4 - 3 = (19 - 13) * 4 - 3 = 21

Tina is 21.

Greeting

asinus :- )

  !