a disc jockey must play 14 commercial spots during 1 hour of a radio show.Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 11 min, how many 30-second commercials were played that hour. How many 60-second commercials.
11 min * 60 s/min = 660 s,
x - 30 s comm,
y - 60 s comm,
x + y = 14 comm,
y = 14 - x,
30x + 60y = 660 s,
Substitute 14 - x for y:
30x + 60(14 - x) = 660,
30x + 840 - 60x = 660,
-60x = 660 - 840
-30x = -180,
x = 6 30 s comm,
6 + y = 14,
y = 8 60 s comm.