The music department of a school sold 750 tickets to the school concert, for a total of \$4755. Students paid \$5 for a ticket and non-students paid \$8 for a ticket. How many non-students attended the concert? I'm not sure what equations to use to get this answer.
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$\begingroup$Basic approach. Think about what you don't know: You don't know how the purchased tickets were distributed amongst students and non-students. So use variables to denote them—$s$ for the number of students who bought tickets, and $n$ for the number of non-students who bought tickets.
What equation would represent the fact that the total number of tickets equals $750$?
Now what expression (not equation) would represent the money spent by students on tickets? For instance, if $s = 7$, then those $7$ students collectively spent $7 \times 5 = 35$ dollars. How would you make that more general, in terms of $s$?
How would you do that for the $n$ non-students?
Then add those two expressions up, and find an equation to represent the fact that the total amount of money spent on tickets equals $4755$ dollars.
Now you have two equations, which you can solve to determine $s$ and $n$, the latter quantity being what you actually want.
$\endgroup$ $\begingroup$You have to put this on equation.
"Students paid $\$$5 for a ticket and non-students paid $\$$8 for a ticket", so the total earned money is $5t_1+8t_2=4755$, where $t1$ is the number of students, and $t_2$ is the number of non-students. Plus, you know that the total number of tickets is $750$, so $t1+t2=750$. You are left with one equation depending only on $t_2$, then you can find $t_2$.
$\endgroup$ $\begingroup$Let $n$ bet the number of student tickets and $N$ be the number of non-student tickets. Then you know that $$ n+N = 750 $$ and $$ 5n+8N=4755 $$ This is two equations with two unknowns.
$\endgroup$ $\begingroup$Let's call the amount of non-students $n$. Then we know the amount of non-students is $750-n$ (since the total number of people is $750$). So all non-students together paid $8\cdot n$ dollar, and all students together paid $(750-n)\cdot 5$ dollars. Together, that is $4755$ dollar, so
$$8n+5(750-n)=4755$$
Now we can simplify this, to get
$$8n+5\cdot 750-5\cdot n=3n+3750=4755$$
so that
$$3n=1005$$
and dividing both sides by $3$ yields
$$n=335$$
so the total number of non-students is $335$.
$\endgroup$ 0 $\begingroup$If all tickets were sold to students they would have gain $5\cdot750= 3750$ bucks. As they gained $4755$ bucks, the remaining income of $1005$ dollars is due the non students. As each of them paid three dollars more then a student there must be $1005:3=335$ non students.
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