Question

for a particular event $743 tickets were sold for a total of $4,819. if students paid $5 per ticket and non students paid $8 per ticket how many student tickets were sold?

Answer 1

`\begin{gathered} \text{ Let x be the number of students, and y the number of non students} \\ \text{ We can use two equations} \\ x+y=743\rightarrow\text{ The number of tickets sold} \\ 5x+8y=4819\rightarrow\text{ Total \$ sold} \\ \text{ Now that we have two equations, we can use substitution from the 1st equation} \\ x+y=743 \\ x=743-y \\ \text{Now substitute this to the 2nd equation} \\ 5x+8y=4819\text{ Subsitute x from the first equation} \\ 5(743-y)+8y=4819 \\ 3715-5y+8y=4819\text{ Simplify the equation} \\ 3y=4819-3715 \\ 3y=1104\text{ Divide both sides by 3} \\ y=368,\text{ now we have the number for non students, let us substitute this} \\ \text{ to get the number of students to equation 1} \\ x+y=743 \\ x+368=743 \\ x=743-368 \\ x=375\text{ the number of students} \\ \text{ We now have 375 of students and 368 of non students} \end{gathered}`