so.. le'ts say he invested "a" amount at 7%.
now, how much is 7% of a? well, (7/100) * a, or 0.07a.
then he invested some more at 12%
in fact "$3000 more than twice the amount" of "a" is what he invested at 12%.
now, what's twice the amount of "a"? well, 2a.
what's 3000 more than that? well, 2a + 3000
so, he invested that much at 12%, how much is 12% of 2a+3000? well, (12/100) * (2a + 3000), or just 0.12(2a+3000)
we also know that, the interest earned from both investments is 4700, thus
0.07a + 0.12(2a+3000) = 4700
[tex]\bf \stackrel{\textit{at 7\%}}{0.07a}+\stackrel{\textit{at 12\%}}{0.12(2a+3000)}=4700\implies 0.07a+0.24a+360=4700
\\\\\\
0.31a=4700-360\implies 0.31a=4340\implies a=\cfrac{4340}{0.31}
\\\\\\
\boxed{a=14000}[/tex]
how much was invested at 12%? well, 2a + 3000.
