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?


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: {{{(a-5)+(b-5)}}}
Twice the sum... {{{2((a-5)+(b-5))=2a+2b-20}}}
Carl five years ago was 3 years less than the above expression, so:


{{{c-5=2a+2b-20-3}}}
{{{c=2a+2b-18}}}


Since {{{a=b-4}}}, {{{b = a+4}}}


Now substitute:
{{{3a=2a+2(a+4)-18}}}


{{{3a=2a+2a+8-10}}}


{{{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.