Final answer:
After setting up a system of equations with T representing the number of television commercials and R representing the number of radio commercials, the equations are solved to find that T = 22. However, this answer does not match any of the provided choices, indicating there may be an error in the question or answer choices. Therefore, the most appropriate option is C.
Step-by-step explanation:
To solve the problem presented by the student, we must set up a system of equations based on the given information:
- The total amount spent on advertising is $97,000.
- The cost of a 1-minute radio commercial is $300.
- The cost of a 1-minute television commercial is $4,000.
- The company plans to have a total of 52 1-minute commercials, which can be either radio or television.
Let's denote the number of television commercials as T and the number of radio commercials as R. We can set up two equations based on these variables:
- Equation 1 (budget constraint): 4,000T + 300R = 97,000
- Equation 2 (total number of commercials): T + R = 52
Now we can solve this system of equations. First, we'll express one variable in terms of the other using Equation 2:
R = 52 - T
Then, we substitute this expression for R into Equation 1:
4,000T + 300(52 - T) = 97,000
Now simplify and solve for T:
4,000T + 15,600 - 300T = 97,000
3,700T = 81,400
T = 20
However, 22 is not one of the answer choices, suggesting there might have been a mistake in the calculations. Let's recheck:
Simplify:
3,700T = 97,000 - 15,600
T = (97,000 - 15,600) / 3,700
T = 81,400 / 3,700
T = 20
Since there is no arithmetic error in this calculation, there isn’t an answer choice that matches our solution, which indicates a possible mistake in the question prompt or the answer choices provided.