Nelson has half investments in stock paying a 6% dividend and the other half paying 9% intereat. if his annual interest is $600 how much does he have invested

He invested "a" at 6% and "b" at 9%

now, how much is 6% of a? well, 6/100 * a or 0.06a
how much is 9% of b? well 9/100 * b or 0.09b

so... both interest yielded $600 in a year
thus, we can say that    0.06a + 0.09b = 600

well, Nelson put half in "a" and half in "b", that means, "a" and "b" are just two equal halves, thus whatever amount he put in "a", is the same exact amount he put in "b", thus a = b   or b = a

so 0.06a + 0.09b = 600 is really
0.06a + 0.09a = 600      <

solve for "a" to see how much he invested in one

how much did he invest total? well 2a