let k be Kaitlin, j be John and c be Carlos. We get that
[tex]\begin{gathered} k+j+c=109 \\ k=c+7 \\ j=4c \end{gathered}[/tex]so we get that
[tex]\begin{gathered} c+7+4c+c=109 \\ 6c=109-7=102 \\ c=\frac{102}{6}=17 \end{gathered}[/tex]so carlos sent 17 messages. Kaitlin sent 24 and John 68