[tex]+\left\{\begin{array}{ccc}A+B=76\\A-B=38\end{array}\right\\---------\\.\ \ \ \ \ \ \ 2A=114\ \ \ \ /:2\\.\ \ \ \ \ \ \ \ A=57\\\\\left\{\begin{array}{ccc}A=57\\A+B=76\end{array}\right\\\left\{\begin{array}{ccc}A=57\\57+B=76\end{array}\right\\\\\left\{\begin{array}{ccc}A=57\\B=76-57\end{array}\right\\\left\{\begin{array}{ccc}A=57\\B=19\end{array}\right\\[/tex]
[tex]A:B=57:19=3[/tex]