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%?

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



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

4+2=-2. 1+2=3. y=-2/3x+b. 2=4/3+b. 2/3=b. the answer is y= -2/3x+2/3