SOLUTION: Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago, Carl's age was 3 years less than twice the sum of the girls' ages then. How old is Carl now

Question 133416: Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago, Carl's age was 3 years less than twice the sum of the girls' ages then. How old is Carl now?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago, Carl's age was 3 years less than twice the sum of the girls' ages then. How old is Carl now?

Alice now: a
Betty now: b
Carl now: c
Alice is 4 years younger than Betty

Carl five years ago: c - 5
Alice five years ago: a - 5
Betty five years ago: b - 5
The sum of the girls' ages five years ago:
Twice the sum...
Carl five years ago was 3 years less than the above expression, so:

Since ,

Now substitute:

So Alice is 10 now, which means that Betty is 10 + 4 = 13, and Carl is 3 * 10 = 30.

Check the answer:
5 years ago, Carl would have been 25, Alice, 5, and Betty, 9. the sum of their ages then would have been 14, twice 14 is 28, 3 years less than that is 25. Answer checks.
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