[tex]K-Karen\ age\\S-Suzanne\ age\\K-4-Karen\ age\ 4\ years\ ago\\S-4-Suzanne\ age\ 4\ years\ ago\\\\ \left\{\begin{array}{ccc}K=S+7\\K-4=2(S-4)\end{array}\right\\\left\{\begin{array}{ccc}K=S+7&(1)\\K-4=2S-8&(2)\end{array}\right\\\\subtitute\ (1)\ to\ (2):\\\\(S+7)-4=2S-8\\S+7-4=2S-8\\S+3=2S-8\ \ \ \ |subtract\ 3\ from\ both\ sides\\S=2S-11\ \ \ |subtract\ 2S\ from\ both\ sides\\-S=-11\\\boxed{S=11}[/tex]
[tex]Put\ the\ value\ of\ S\ to\ (1):\\\\K=11+7\\\boxed{K=18}\\\\\left\{\begin{array}{ccc}K=18\\S=11\end{array}\right\\\\Answer:\ Karen\ does\ 18\ years\ and\ Susanne\ does\ 11\ years.[/tex]
