Question

353 people attend a local play at a private club. members get tickets for $2.75, while non-members must pay $6.50. if the total gate for the play came to $1762, how many members and non-members came to the play

Answer 1

We will be dealing with a system of equations and we'll find the answer by using elimination.
M= members and N= non-members
M+N=353
2.75M+6.50N=1762
We can eliminate M by multiplying the first equation by -2.75.
-2.75m-2.75n=-970.75
2.75m+6.50N=1762
3.75n=791.25
Now divide
791.25/3.75=211
So there was 211 non-member tickets. All we have to do to find the number of member tickets is replace n with its value.
211+m=353
353-211=m=142
There are 142 member tickets. To check our answer, let's put both values in for the second equation.
2.75(142)+6.50(211)
390.50+1,371.50
1762
So, there were 142 members and 211 non-members that came to the play.