Let the rate for the $800 investment be q and
let the rate for the $1100 be r.
Therefore,
[tex]r=q+0.04------------(1)[/tex][tex]800q+1100r=117----------(2)[/tex]Substituting equation (1) into equation (2), we have
[tex]\begin{gathered} 800q+1100(q+0.04)=117 \\ 800q+1100q+44=117 \\ 1900q=73 \\ \text{ Hence} \\ q=\frac{73}{1900}\approx0.038 \\ \text{ therefore,} \\ r=0.038+0.04 \\ r=0.078 \end{gathered}[/tex]Hence the rate for the $800 investment is 3.8% and
the rate for the $1100 investment is 7.8%
