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 Question from George: 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.

Hi George,

This is what you sent us

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.

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.

Penny

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