she invested "a" at 5% and "b" at 6%.
now, we know whatever amounts "a" and "b" are, they add up to 8000, thus a + b = 8000.
how much is 5% of a? well, (5/100) * a, or 0.05a.
how much is 6% of b? well, (6/100) * b, or 0.06b.
After a year, their combined interest, their yield, was 455, thus, we also know that 0.05a + 0.06b = 455.
[tex]\bf \begin{cases}
a+b=8000\implies \boxed{b}=8000-a\\
0.05a+0.06b=455\\
----------\\
0.05a+0.06\left( \boxed{8000-a} \right)=455
\end{cases}
\\\\\\
0.05a-0.06a+480=455\implies -0.01a=-25\implies a=\cfrac{-25}{-0.01}
\\\\\\
\boxed{a=2500}[/tex]
how much was invested at 6%? well, b = 8000 - a.
