Verified Answer :

\(+\left\{\begin{array}{ccc}a+b=76\\a-b=38\end{array}\right\\-----------\\.\ \ \ \ \ \ \ 2a=114\ \ \ \ \ |:2\\.\ \ \ \ \ \ \ \ \ \ a=57\\\\57+b=76\\b=76-57\\b=19\\\\\frac{a}{b}=\frac{57}{19}=\fbox{3}\)

MattD

First we need to calculate how much is a and b, from the first and second equations, and then we take care of each other:
a + b = 76
a - b = 38
a / b = ?

\(\begin{cases}a+b=76\\a-b=38\end{cases}|+\)
\(a+a+b-b=76+38\)
\(2a=114|:2\)

\(a=57\)
\(a+b=76\)
\(57+b=76\)
\(b=76-57=19\)

\(\frac{a}{b}=\frac{57}{19}=3\)