SOLUTION: 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

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Question 148366: 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 minutes how many 30 second commercials were played that hour? How many 60 second commercials?
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
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 minutes how many 30 second commercials were played that hour? How many 60 second commercials?

the total commercial time during 1 hour is 11 minutes
Convert 11 minutes to seconds
660 seconds

x=amount of 30 second commercials
y=amount of 60 second commercials

30x+60y=660

a disc jockey must play 14 commercials

x+y=14

So you have
30x%2B60y=660
x%2By=14

Use the second equation and solve for x.
x%2By=14 becomes x=14-y

Plug that in for x in the first equation.
30%2814-y%29%2B60y=660

Distribute
420-30y%2B60y=660

Combine like terms
420%2B30y=660

Subtract 420 from both sides
30y=240

Divide by 30
y=8

plug that in for y in the second original equation
x%2B8=14
x=6

Check: 30x%2B60y=660
30%286%29%2B60%288%29=660
180%2B480=660
It's true!

So the dj played 6 thirty-second commercials and 8 sixty-second commercials