Here is my Question, Answer and Solution

Question:

Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice as old as her sister.

Find the present age of the two siblings.

Answer:

Theresa is now 20 years of age and Joni is now 16 years of age

Solution:

Translate the information into a workable equation.

Begin by choosing a variable to work with and saying what it represents, usually one of the numbers we are trying to find.

Let J = Joni's present age

Next, use one of the relationships between Joni and her sister to conclude her sister's age.

Let J+4 = Theresa's present age (She is 4 years older than Joni)

Next, use the other relationship between Joni and her sister to set up an equation.

Let (T - 12) = 2 (J - 12) (12 years ago Theresa was twice as old as Joni was).

Solve for J using the elimination and/or the substitution method for simultaneous equations

and use to find T:

(T - 12) = 2 (J - 12)

Substitute J+4 for T

((J+4) - 12) = 2(J - 12)

J+4 - 12 = 2J - 24

J + 8 = 2J - 24

J = 24 - 8 = 16

T = J + 4 = 16 + 4 = 20

Cross check:

T - 12 = 20 - 12 = 8 (Theresa's age 12 years ago)

J = J - 12 = 16 - 12 = 4 (Joni's age 12 years ago)

Theresa is twice as old as Joni

Is the solution correct?

George

I agree with your solution except for the line I highlighted in red. It should be J - 8 = 2J - 24. I think it was just a typo on your part.