Question

Martina invested her savings in two investment funds. The $12,000 that she invested in Fund A returned a 5% profit. The amount that she invested in Fund B returned a 1% profit. How much did she invest in Fund B, if both funds together returned a 4% profit?

Answer 1

we know she invested 12000 in A, and say "b" dollars in B, so the total amount invested or principal must be 12000 + b.

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{3em}\underset{\textit{\Large profit from A}}{\stackrel{\textit{5\% of 12000}}{\left( \cfrac{5}{100} \right)12000}}\implies 600~\hfill \underset{\textit{\Large profit from B}}{\stackrel{\textit{1\% of "b"}}{\left( \cfrac{1}{100} \right)b}\implies 0.01b}$

we also know that those profits added together, yielded only 4% of the total amount invested, namely 4% of (12000 + b), which will be 0.04(12000 + b).

$\bf \stackrel{\textit{\Large returned profits}}{\stackrel{A}{600}+\stackrel{B}{0.01b}~~=~~0.04(12000+b)}\implies 600+0.01b=480+0.04b \\\\\\ 120+0.01b=0.04b\implies 120=0.03b\implies \cfrac{120}{0.03}=b\implies \boxed{4000=b}$