Algebra word problem help

Chapman Universitys football team sold a total of 456 tickets to their games. A regular ticket costs $3.50. A student ticket costs $1.00. A faculty ticket costs $2.00. Ticket sales totaled $1206. How many tickets of each kind were sold? Twice as many students attended as faculty members.

x = students x = 2k
k = fac. members k = 2x
y= others

2k + k + y = 456
2k *1 + k*2 + y * 3.5 = 1206

y = 456 -3k
4k + (456 - 3k)*3.5 = 1206
6.5 k =390 ==> k = 60
x = 2k = 120
y = 456 - 180 = 276

R+s+f=456

2s=f

Substitute

3s+r=456
r=456-3s

3.5r+1s+2f=$1206

3.5r+5s=1206
3.5(456-3s)+5s=1206
1596-10.5s+5s=1206
390=5.5s

S=70.90

F=141.81

R=245