For commercials aired during a sporting​ event, advertisers paid an average of​ $5 million to air a​ 30-sec commercial.

Question

For commercials aired during a sporting​ event, advertisers paid an average of​ $5 million to air a​ 30-sec commercial. Even at this​ rate, some commercials were longer than 30 sec. A total of 60 commercials ran for either 30 sec or 1 min. The total running time was 38 1/2 min. How many of each length commercial aired during the sporting​ event?

Answer 1

lets say;

x is # of 30sec commercials

y is # of 1 min commercials (30sec = 0.5 min)

x + y = 60

0.5x +y = 38.5.

one of the way is to cancel y values,

we can multiply second equation by -1 and we have -0.5x -y = -38.5

x + y = 60

-0.5x -y = -38.5

y cancels out and we have

0.5x = 60 - 38.5 = 21.5

if half of x is 21.5 then x = 43

x +y = 60; 43 +y = 60; y = 17

# of 30 sec commercials is 43;

# of 1min commercials is 17;