A disc jockey must play 14 commercial spots during one hour of 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?
and thanks for everyones help I am having bad problems with this
8 sixty-second commercials = 8 minutes
6 thirty-second commercials = 3 minutes
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To solve this problem, we will use a system of equations. Let's assign variables to represent the number of 30-second commercials and 60-second commercials.
Let x be the number of 30-second commercials.
Let y be the number of 60-second commercials.
We know that the total number of commercials is 14, so we can write the equation:
x + y = 14
We also know that the total commercial time is 11 minutes, which is equivalent to 11 * 60 seconds.
The total time for the 30-second commercials is 30x seconds, and the total time for the 60-second commercials is 60y seconds.
So, we can write another equation:
30x + 60y = 11 * 60
Now we have a system of equations:
x + y = 14
30x + 60y = 11 * 60
To solve this system, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From the first equation, we can express x in terms of y:
x = 14 - y
Substituting this value of x into the second equation:
30(14 - y) + 60y = 11 * 60
420 - 30y + 60y = 660
420 + 30y = 660
30y = 240
y = 8
Substituting this value of y back into the first equation:
x + 8 = 14
x = 6
Therefore, there were 6 thirty-second commercials played and 8 sixty-second commercials played.