Gary won $70,000 in the lottery after all tax deductions. he invested part of the money at 11% and deposited the remainder in tax-free bonds at 12%. his total annual income from the investments was $7900. find the amount invested at 11%. find the amount invested at 12%.

So... the amounts Gary invested are... hmm say "a" and "b", at 11% and 12% respectively

we know he invested the whole 70,000, so  whatever "a" and "b" are,
a + b = 70,000

what's 11% of a? well 11/100 * a or 0.11a <-- that's how much he earned in interests from that investment

what's 12% of b? well 12/100 * b, or 0.12b <-- that's how much he earned in interests from that investment

whatever 0.11a and 0.12b are, we know they total 7,900
so..... 0.11a + 0.12b = 7,900

thus   

solve for "b", to see how much he invested at 12%

what about the 11% investment? well a = 70,000-b