question below

Question

Tickets to Wine Weekend cost $160 on the night of the reception and $140 if purchased in advance. If 150 tickets were sold for a total $21,800, how many of the tickets were sold in advance?

 

Need two equations

Answer 1

A = Advanced Sales tickets

N = Night-of-Performance tickets

 

1)   A * 140 + N * 160 = 21,800

2)   A + N = 150

 

You can either use elimination, or substitution [N = 150 - A, from eq. 2. substitute into equation 1.)

 

I prefer elimination, personally)

 

multiple Eq.2 by 160

 

2') 160A + 160N = 24,000

 

Subtract 1 from 2'

 

    160A + 160N = 24,000

 -( 140A + 160N = 21,800  )

  ----------------------------

       20A            = 2200

therefore A = 110 tickets