How old are you if you are twice as old as your sister is and Next year she will be three times the age you were thirteen years ago?

Answer 1

There are two variables in this situation: your age, and your sister's age. Your age will be known as x, and your sister's will be known as y.

Now you can put the given information into equation form:

Your age = Twice your sister's age

x = 2y

One year from now, your sister will be 3 times your age minus thirteen years.

y + 1 = 3(x - 13)

Since x is clearly the same as 2y, you can substitute that into the second equation, then solve.

y + 1 = 3(2y - 13) --- Substitute 2y

y + 1 = 6y - 39 --- Distribute 3

y + 40 = 6y --- Move constants to one side and add

40 = 5y --- Move variables to one side and add

8 = y --- Divide

Your sister is 8 years old. Now, to find your age, simply set y = 8 in the first equation and solve.

x = 2(8) = 16

You are 16 years old.