Heather downloaded some television shows. a sitcom is 0.3 gigabyte; a drama, 0.6 gigabyte; and a talk show, 0.6 gigabyte. she downloaded 7 programs totaling 3.6 gigabytes. there were twice as many episodes of drama as the sitcom. how many episodes of each show did she download?

Variables:

sitcom episodes: s
drama episodes: d
talk show episodes: t

0.3 s + 0.3 d + 0.6 t = 3.6
s + d + t = 7
d = 2s

From s + d + t = 7  and d = 2s
     s + 2s + t = 7
     3s + t = 7
     t = 7 - 3s

substitute t = 7 - 3s and d = 2s in 0.3 s + 0.3 d + 0.6 t = 3.6

0.3s + 0.3(2s) + 0.6 (7 - 3s) = 3.6

0.3s + 0.6s + 4.2 - 1.8s = 3.6

- 0.6 s = 3.6 - 4.2
-0.6 s = - 0.6

s = 1. Then

d = 2s = 2

t = 7 -3(s) = 7 - 3(1) = 4

1 sitcom, 2 drama and 4 talk show.