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 min, how many 30 seconds commercials were played that hour. how many 60 second commercials?

Let x = # 30 second commercials.

let y = # 60 second commercials.
Two equations can be written.
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30x + 60y = 11*60
x + y = 14
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Solve for x and y.
Post your work if you get stuck.

To find the number of 30-second commercials and 60-second commercials played during the hour, we can use algebraic reasoning.

Let's assume the number of 30-second commercials played is x, and the number of 60-second commercials played is y.

We know that the total number of commercials played is 14:
x + y = 14

We also know that the total commercial time during 1 hour is 11 minutes, which is equal to 11 * 60 seconds = 660 seconds. Using this information, we can create a second equation based on the time spent on each commercial:
30x + 60y = 660

Now we can solve this system of equations.

1. Multiply the first equation by 30 to eliminate x:

30(x + y) = 30 * 14
30x + 30y = 420

2. Subtract the second equation from the equation obtained in Step 1:

(30x + 30y) - (30x + 60y) = 420 - 660
30x + 30y - 30x - 60y = -240

Combine like terms:

-30y = -240

3. Divide both sides of the equation by -30 to solve for y:

-30y / -30 = -240 / -30
y = 8

So, the number of 60-second commercials played is 8.

4. Now substitute the value of y back into the first equation to solve for x:

x + 8 = 14
x = 14 - 8
x = 6

Therefore, the number of 30-second commercials played is 6.

To summarize:

The disc jockey played 6, 30-second commercials during the hour, and 8, 60-second commercials.