a = amount invested at 10%
b = amount invested at 18%
now, she has 138,400 bucks burning her pockets, so, whatever "a" and "b" are, we know that a + b = 138400.
how much is 10% of a? well, (10/100) * a, or 0.10a.
how much is 18% of b? well, (18/100) * b, or 0.18b.
she would like to have an income, namely an interest yield, from her investements of 18720 combined, thus, we know that 10% of a and 18% of b, will need to be that much, thus 0.10a + 0.18b = 18720.
[tex]\bf \begin{cases}
a+b=138400\implies \boxed{b}=138400-a\\
0.10a+0.18b=18720\\
-----------------\\
0.10a+0.18\left( \boxed{138400-a} \right)=18720
\end{cases}
\\\\\\
0.10a-0.18a+24912=18720\implies -0.08a=-6192
\\\\\\
a=\cfrac{-6192}{-0.08}\implies a=77400[/tex]
how much will it be for b? well, b = 138400 - a.
