How do I derive the aggregate demand function given two utilities functions?

Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$.

I’m being asked to derive the aggregate demand function. The only thing I got so far was finding the market demand for each good per person, which is

$x^*_1 = {I_1}/2P_x$ , $y^*_1 = {I_1}/2P_y$, for person 1

$x^*_2 = {I_2}/2P_x$, $y^*_2 = {I_2}/2P_y$ for person 2

Am I missing something? Please help.

Thanks.