SOLUTION: Antonette age is 3 years older than her sister. 6 years ago her sister is 4 times antonette age. How old is antonette?

Question 1149530: Antonette age is 3 years older than her sister. 6 years ago her sister is 4 times antonette age. How old is antonette?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The statement of the problem is faulty; it says now Antonette is older and 6 years ago her sister was older.

I will ignore that and solve the problem as it was probably intended -- with Antonette older.

Using formal algebra... which I will assume is what you are learning to do by asking this question....

Let the sister's age be x
Then Antonette's age is x+3

Then 6 years ago the sister's age was x-6, and Antonette's age was (x+3)-6 = x-3.

Then, since 6 years ago Antonette was 4 times as old as her sister,

ANSWER: Antonette's age is x+3 = 10 years

CHECK: 6 years ago, Antonette was 10-6 = 4 years old and her sister was 7-6 = 1 year old; Antonette was 4 times as old as her sister.

Note that, if a formal algebraic solution is not required, the question can be answered quickly with a little logical reasoning and simple arithmetic.

If the difference between their ages is 3 years, then when Antonette was 4 times as old as her sister, their ages had to be 4 and 1.

And since that was 6 years ago, their ages now are 10 and 7.

While knowing how to solve problems like this with formal algebra is important, solving them using logical reasoning is also good mental exercise.

RELATED QUESTIONS
Jennifer is 6 years older than her sister Janette. 4 years ago she was 4 times as old as... (answered by macston)

Caridad is 6 years older than her sister. Four years ago she was 4 times as old as her... (answered by drj)

Four years ago a woman was three times as old as her sister. in five years time she will... (answered by ankor@dixie-net.com)

Caridad is six years older than her sister. Four years ago she was 4 times as old as her... (answered by ptaylor)

Julie is 3 years younger than twice her sisters age was 6 years ago. What age is her... (answered by josmiceli)

Sharon's sister is 9 years older than her. Their combined age is 35. How old is Sharon's... (answered by Alan3354)

You're four years older than your 18 year old sister. How many years ago were you three... (answered by Maths68)

Joan is twice as old as her sister now. What is her age 6 years... (answered by math_tutor2020)

Ten years ago Emily's age was 4 times bigger than her sister's. If the age of her sister... (answered by Alan3354,josgarithmetic,ikleyn)