Question

Laura is 3 times as old as Maria was when Laura was as old as Maria is now. In 2 years Laura will be twice as old as Maria was 2 years ago. How old are they now?

Answer 1

Answer:

Laura is 30 years old and Maria is 18 years old.

Step-by-step explanation:

Let x be the present age of Laura and y be that of Maria.

Laura was 3 times older than Maria when Laura had Maria's present age.

Lets say Laura had Maria's present age(y) k years before.Then Maria's age at that time will be y-k where k=(x-y).

Then:

y=3(y-k)

y=3(y-(x-y))

y=3(2y-x)

3x=5y  -------1

After two years Laura will become x+2 years old and 2 years ago Maria was y-2 years old. Then:

x+2=2(y-2)

x=2y-6--------2

Solving 1 and 2 we get:

x=30 and y=18

Hence Laura's present age is 30 and Maria's present age is 18.