SOLUTION: Can someone help me please? Word problems are the worst! A disc jockey plays 12 commercial spots during 1 hr. of radio show. Each commercial is either 30 or 60 sec. long. If the

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Question 193182: Can someone help me please? Word problems are the worst!
A disc jockey plays 12 commercial spots during 1 hr. of radio show. Each commercial is either 30 or 60 sec. long. If the total commercial time in one hr. is 8 min. how many 30 sec. commercials were played that hr.? How many 60 sec.?
Thanks a lot
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
perhaps this will help......first step is to search what the problem is asking for
This problem wants to know how many 30 sec and 60 sec commercials there are. Now label the unknowns. Lets call the 30 and 60 sec spots a and b respectively
:
Now try to come up with 2 equations since we have 2 unknowns
:
we are told that there are 12 commercial spots so
:
a+b=12.............eq 1
we know that the total time for commercials is 8 minutes
We must make sure both of these are in the same unit....commercials are in seconds so lets convert to minutes before we write the equation..30 sec =1/2 min and 60 sec =1 minute
:
(1/2)a+b=8.......eq 2
:
rewrite eq 1 to a=12-b and plug this into eq 2
:
(1/2)(12-b)+b=8
:
6-(1/2)b+b=8
:
(1/2)b=2
:
b=4 (60 second spots)
:
a=12-b=12-4=8 (30 second spots)