Given the equation:
[tex]10a+8c=76[/tex]If Jacob bought 4 adult tickets, then a = 4, so we can solve for c:
[tex]\begin{gathered} a=4 \\ \Rightarrow10(4)+8c=76 \\ \Rightarrow8c=76-40=36 \\ \Rightarrow c=\frac{36}{8}=\frac{9}{2}=4.5 \\ c=4.5 \end{gathered}[/tex]therefore, Jacob bought 4 or 5 students tickets.
Now, if Jacob bought 2 student tickets, then c=2 and for 'a' we have the following:
[tex]\begin{gathered} c=2 \\ \Rightarrow10a+8(2)=76 \\ \Rightarrow10a=76-16=60 \\ \Rightarrow a=\frac{60}{10}=6 \\ a=6 \end{gathered}[/tex]therefore, Jacob bought 6 adult tickets.
Finally, to find the equation that shows the number of student tickets as a function of adult tickets, we have to solve for 'c' to get the following:
[tex]\begin{gathered} 10a+8c=76 \\ \Rightarrow8c=76-10a \\ \Rightarrow c=-\frac{10}{8}a+\frac{76}{8}=-\frac{5}{4}a+\frac{19}{2} \\ c=-\frac{5}{4}a+\frac{19}{2} \end{gathered}[/tex]therefore, the function would be c = -5/4a +19/2