Question

Roberto invested some money at 7%, and then invested $3000 more than twice the amount at 12%. His total annual income from the two investments was $4700. How much was invested at 12%?

Answer 1

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



`\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}`

how much was invested at 12%? well, 2a + 3000.