Emma has half of her investments in stock paying a 9% dividend and the other half in a stock paying 11% interest. if her total annual interest is $420, how much does she have invested?

X/2 x .09 =y
x/2 x .11= z

y + z = 420
((x/2) x .09) + ((x/2) x .11) = 420

.09x/2 + .11x/2 = 420
.2x/2= 420
.1x=420
x=4200

Plug that value back into the originals to check

4200/2 x .09 = 189
4200/2 x .11 = 231
                     
                     420

She invested 4200 dollars