Let's calculate the total number of children, adults, and teens
[tex]\begin{gathered} =77+73+119 \\ =269 \end{gathered}[/tex]
To calculate a total number for chocolate, we will have that
[tex]\begin{gathered} \text{total number=total chocolate+total vanilla+total neither} \\ 269=\text{total chocolate+92+70} \\ 269=\text{total chocolate+162} \\ \text{total chocolate=269-162} \\ \text{total chocolate=107} \end{gathered}[/tex]
Let's calculate the number of teens that like chocolate
[tex]\begin{gathered} \text{total chocolate=choc(Child})+choc(Teen)+choc(adult)_{} \\ 107=40+\text{choc(teen)}+55 \\ 107=95+\text{choc(teen)} \\ \text{choc(teen)}=107-95 \\ \text{choc(teen)}=12 \end{gathered}[/tex]
Let's calculate the number of children that like vanilla
[tex]\begin{gathered} \text{total Children=choc(Child)+vanilla(Child)+neither(Child)} \\ 77=40+\text{vanilla(Child)}+15 \\ 77=55+\text{vanilla(Chilld)} \\ \text{Vanilla(Child)}=77-55 \\ \text{Vanilla(Child)}=22 \end{gathered}[/tex]
Let's calculate the number of adults that like vanilla
[tex]\begin{gathered} \text{Total vanilla=vanilla(Child)+vanilla(T}een)+vanilla(adult) \\ 92=22+16+\text{vanilla(adult)} \\ 92=38+\text{vanilla(adult)} \\ \text{vanilla (adult)=92-38} \\ \text{vanilla(adult)}=54 \end{gathered}[/tex]
Finally, we will calculate the number of adults that like neither
[tex]\begin{gathered} \text{Neither(total)}=\text{neither(Child)}+\text{neither(Te}en)+Neither(adult) \\ 70=15+45+\text{neither(adult)} \\ 70=60+\text{neither adult} \\ \text{neither(adult)}=70-60 \\ \text{neither (adult)=10} \end{gathered}[/tex]
