Final answer:
To find the number of 30 second commercials, we can set up a system of equations using the total number of commercial breaks and the total time of the commercials. Solving the system, we find that there are 4 commercials that are 30 seconds long.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x be the number of 30 second commercials, and y be the number of 1 minute commercials.
We know that there are 12 commercial breaks in total. So, we can write the equation x + y = 12.
We also know that the total time of the commercials is 10 minutes. Since each 30 second commercial contributes 30/60 = 1/2 minute to the total time, and each 1 minute commercial contributes 1 minute, we can write the equation (1/2)x + 1y = 10.
Now, we can solve this system of equations to find the values of x and y. Multiplying the first equation by 1/2, we get (1/2)x + (1/2)y = 6. Subtracting this equation from the second equation, we get 1/2y = 4, which implies y = 8. Substituting this value back into the first equation, we get x + 8 = 12, so x = 4.
Therefore, there are 4 commercials that are 30 seconds long.