a = amount invested at 4%.
b = amount invested at 9%.
we know the total amount invested was $26500, thus a + b = 26500.
whatever% of anything is just (whatever/100) * anything.
how much is 4% of a? well, is just (4/100) * a, or 0.04a.
how much is 9% of b? well, is just (9/100) * b, or 0.09b.
we know the interest yielded for both amounts adds up to $1510, thus 0.04a + 0.09b = 1510.
[tex]\bf \begin{cases}
a+b=26500\implies \boxed{b}=26500-a\\
0.04a+0.09b=1510\\
----------------\\
0.04a+0.09\left( \boxed{26500-a} \right)=1510
\end{cases}
\\\\\\
0.04-0.09a+2385=1510\implies -0.05a=-875
\\\\\\
a=\cfrac{-875}{-0.05}\implies a=17500[/tex]
how much was invested at 9%? well, b = 26500 - a.
