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

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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?
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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
a=b-4 Alice is 4 years younger than Betty
c=3a

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: %28a-5%29%2B%28b-5%29
Twice the sum... 2%28%28a-5%29%2B%28b-5%29%29=2a%2B2b-20
Carl five years ago was 3 years less than the above expression, so:

c-5=2a%2B2b-20-3
c=2a%2B2b-18

Since a=b-4, b+=+a%2B4

Now substitute:
3a=2a%2B2%28a%2B4%29-18

3a=2a%2B2a%2B8-10

3a=4a-10
-a=-10
a=10

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.