SOLUTION: Mark is 8 years older than his sister Rita. Four years ago rita was two thirds as old as Mark. How old are they now?

Question 1169961: Mark is 8 years older than his sister Rita. Four years ago rita was two thirds as old as Mark. How old are they now?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Rita is x
Mark is x+8
four years earlier x-4 and x+4 respectively
(x-4)/(x+4)=2/3. cross-multiply
3x-12=2x+8
x=20 Rita
x+8=28 Mark
4 years earlier it was 16/24 and that is 2/3
they are 20 and 28 years old.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution from the other tutor uses a perfectly good standard algebraic method. You should understand how to set up and solve the problem by that method.

I personally prefer a different method for solving a problem like this.

Take a look at the following solution method and see if it "works" for you.

Mark is 8 years older than Rita.

4 years ago she was 2/3 as old as him. Think of that ratio of their ages as a fraction and write it as an equivalent fraction in which the difference between their ages is 8:

That shows you that, when Rita was 2/3 as old as Mark, their ages were 16 and 24.

And since that was 4 years ago, their ages now are 20 and 28.

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