[tex]x-Charlie\ age\\y-Marty\ age\\\\Chrlie\ is\ 24\ years\ older\ than\ Marty:x=y+24\\The\ total\ years\ old\ of\ both\ are\ 130:x+y=130\\\\Therefore\ we\ have:\\ \left\{\begin{array}{ccc}x=y+24&(1)\\x+y=130&(2)\end{array}\right\\\\subtitute\ (1)\ to\ (2):\\\\(y+24)+y=130\\y+24+y=130\\2y+24=130\ \ \ \ |subtract\ 24\ from\ both\ sides\\2y=106\ \ \ |divide\ both\ sdies\ by\ 2\\\boxed{y=53}[/tex]
[tex]Subtract\ the\ value\ of\ y=53\ to\ the\ (1):\\\\x=53+24=\boxed{77}\\\\\boxed{ \left\{\begin{array}{ccc}x=77\\y=53\end{array}\right}\\\\Answer:\\Charlie\ age:77\\Marty\ age:53[/tex]
