Claudia, let's figure this out!
Let's let x = the # of $5 tix, y = the # of $10 tix, and z = the # of $15 tix.
We are told that x + y + z = 180.
We are also told that x + z = 2y.
The last thing we are told is that 5x + 10y + 15z = 1900
What happens if we take the first equation and subtract y from both sides? x + z = 180 - y, right?
Since x + z = 180 - y from the first equation and x + z = 2y in the 2nd equation, then 180 - y = 2y. Solving for y, we get y = 60
Plugging that into the the 2nd equation, we get that x + z = 2(60), so x + z = 120, so x = 120 - z.
Plugging both the y value and the x "value" into the 3rd equation, we get 5(120 - z) + 10(60) + 15z = 1900.
Distributing, we get 600 - 5z + 600 + 15z = 1900.
1200 + 10z = 1900
10z = 700
z = 70
x + y + z = 180
x + 60 + 70 = 180
x + 130 = 180
x = 50
Let's check. 50 $5 tix = $250. 60 $10 tix = $600. 70 $15 tix = $1050. 250 + 600 + 1050 = 1900. Check!
Hope this helps!
