An amateur drama company were selling tickets for their latest production. the opening night was a sell out with all 200 tickets being sold. Tickets were priced as follows:

Adults $9.50 each
Children $4.50 each
Senior citizens $3.50 each

The takings for the opening night amounted to $1375. Also, there were three times as many children's tickets sold as there were senior citizens' tickets.

a) construct a system of linear simultaneous equations to represent this purchase of tickets for the opening night. Determine algebraically the number of each type of ticket sold for the opening night.

Question

An amateur drama company were selling tickets for their latest production. the opening night was a sell out with all 200 tickets being sold. Tickets were priced as follows:

Adults               $9.50 each
Children            $4.50 each
Senior citizens   $3.50 each

The takings for the opening night amounted to $1375. Also, there were three times as many children's tickets sold as there were senior citizens' tickets.

a) construct a system of linear simultaneous equations to represent this purchase of tickets for the opening night. Determine algebraically the number of each type of ticket sold for the opening night.

anonymous · Answer

@Mertsj

anonymous · Answer

I'm having trouble with constructing the linear simultaneous equations.
one of them will be this I believe but I'm unsure about the rest.

a=adults, c=children, s=senior
9.50a+4.50c+3.50s =1375

mertsj · Answer

And c = 3s

mertsj · Answer

And a + c + s = 200

mertsj · Answer

So in yours two equations, replace c with 3s and solve the system.

anonymous · Answer

kk. let me try it. I also got a + c + s = 200 but then I was unsure about the c=3s because I thought it was a + 3s + s = 200, it's really confusing for me.

mertsj · Answer

Right.  It is.  So a + 4s = 200

anonymous · Answer

yes, I solved it correctly. I just had trouble with figuring out the equations, thanks so much!

mertsj · Answer

yw