Answer:
n = 12$ x = 8$ y = 10$ where n, x, and y are number of tickets
12 n + 8 x + 10 y = 3920 and n + x + y = 420
12n + 8 (x + y) + 2 y = 3920
12 n + 8 (5 n) + 2 y = 3920 since 5 (x + y) = n
52 n + 2 y = 3920 or y = 1960 - 26 n
Also, n + x + y = 420 or n + 5 n = 420 since x + y = 5 n
n = 70 so 70 of the $12 were sold
And since y = 1960 - 26 n we have y = 140 tickets
Now 12 * 70 + 8 x + 140 * 10 = 3920
This gives x = 210 tickets
Check: 210 + 140 + 70 = 420 tickets
Also, 12 * 70 + 210 * 8 + 140 * 10 = 3920
