ALGEBRA…………………………………?

crazy hair: ALGEBRA…………………………………?
The band sold 15 adult tickets and 40 tickets to their concert and earned $ 320. For their second concert they sold 25 adult and 50 student tickets and earned $ 450 . How much was an adult ticket?

Answers and Views:

Answer by Sonic Happy New Year 2011
Call x are tickets for adult and y are tickets for others ( x;y ∈ Z )
First : 15 adult tickets and 40 tickets = $ 320
=> 15x + 40y = 320 (1)
Second : 25 adult and 50 student tickets = $ 450
=> 25x + 50y = 450 (2)

From (1) and (2)
{ 15x + 40y = 320
{ 25x + 50y = 450

{ 75x + 200y = 1600
{ -75x – 150y = -1350
Add of them
=> 50y = 250
<=> y = 5

Use y = 5 in 15x + 40y = 320
<=> 15x + 40.5 = 320
<=> 15x + 200 = 320
<=> 15x = 320 – 200
<=> 15x = 120
<=> x = 120 / 15
<=> x = 8

So an adult ticket is 8$