SOLUTION: Ten years ago, Anne was half as old as Sylvia was then. Five years from now, Anne will be as old as Sylvia was five years ago. How old is Sylvia now?

Question 1198719: Ten years ago, Anne was half as old as Sylvia was then. Five years from now, Anne will be as old as Sylvia was five years ago. How old is Sylvia now?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Dozens of ways to set this up; I hope you will get responses other than mine so you can see a variety of ways.

My preference is always to find a way to set the problem up for solving using a single variable.

With the way the information is given in this problem, here is my preferred way of solving the problem.

Ten years ago, Anne was half as old as Sylvia was then:

let x = Anne's age 10 years ago
then 2x = Sylvia's age 10 years ago

Anne's age 5 years from now will be the same as Sylvia's age 5 years ago:

Anne's age 5 years from now is x+15 ("5 years from now" is 15 years after "10 years ago")
Sylvia's age 5 years ago was 2x+5 (5 years after "10 years ago")
x+15 = 2x+5
10 = x

How old is Sylvia now?
10 years older than she was 10 years ago: 2x+10 = 2(10)+10 = 30

ANSWER: Sylvia is 30 years old

CHECK:
Sylvia is 30; 10 years ago she was 20; 10 years ago Anne was 10 (half as old as Sylvia was then); Anne is now 10+10 = 20; 5 years from now Anne will be 25; 5 years ago Sylvia was 30-5 = 25

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