a disk jockey must play 14 commercial spots during one hour of radio show, each commercial is eiter 30 seconds or 60 seconds long. If the total commercial time during one hour is 11 minutes, then ow many 30 second commercials were played that hour?
x of 30 sec so (14-x) are 60 sec
11*60 = 660 sec
so
30 x + 60(14-x) = 660
870 - 30 x = 660
30 x = 210
x = 7
short commercial --- x
long commercial ---- y
x+y = 14 , #1
30x + 60y =11(60)
x + 2y = 22 , #2
#2 - #1
y = 8
then x = 6
6 shorts , 8 long
check : 6+8 = 14
30(6) + 60(8) = 180+480 = 660 = 11(60)
x of 30 sec so (14-x) are 60 sec
11*60 = 660 sec
so
30 x + 60(14-x) = 660
840 - 30 x = 660
30 x = 180
x = 6
To solve this problem, we need to determine the number of 30-second commercials played during the hour.
Let's denote the number of 30-second commercials as 'x' and the number of 60-second commercials as 'y'.
We have two pieces of information:
1. Each commercial is either 30 seconds or 60 seconds long.
2. The total commercial time during one hour is 11 minutes.
From the first piece of information, we can create an equation:
x + y = 14 (since the total number of commercials is 14)
Now, let's convert the total commercial time from minutes to seconds:
11 minutes = 11 * 60 seconds = 660 seconds
From the second piece of information, we can create another equation:
30x + 60y = 660 (since the total commercial time is the sum of all commercial lengths)
Now, we have a system of equations:
x + y = 14
30x + 60y = 660
To solve this system of equations, we can use substitution or elimination method.
Let's use substitution:
From the first equation, we have:
x = 14 - y
Substituting this value of x into the second equation:
30(14 - y) + 60y = 660
420 - 30y + 60y = 660
30y = 660 - 420
30y = 240
y = 8
Substituting the value of y back into the first equation:
x + 8 = 14
x = 14 - 8
x = 6
Therefore, there were 6 thirty-second commercials played during the hour.