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.