a = amount invested at 13%
b = amount invested at 7%
how much is 13% of a ? well is (13/100) * a or 0.13a.
how much is 7% of b ? well is (7/100) * b or 0.07b.
we know the interest earned by a is whatever b is plus 188.65, since it exceeds it by that much, so 0.13a = 0.07b + 188.65.
we also know that both amounts must add up to 4845, thus a + b = 4845.
[tex] \bf \begin{cases}
a+b=4845\implies \boxed{b}=4845-a\\
0.13a=0.07b+188.65\\
---------------\\
0.13a=0.07\left( \boxed{4845-a} \right)+188.65
\end{cases}
\\\\\\
0.13a=339.15-0.07a+188.65\implies 0.20a=527.8
\\\\\\
a=\cfrac{527.8}{0.20}\implies a=2639 [/tex]
so, what is b anyway? well b = 4845 - a.
