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A company plans to spend exactly $97,000 annually for advertising. A 1-minute radio commercial costs $300, and a 1-minute television commercial costs $4,000. If the company has a total of 52 1-minute television and radio commercials, how many 1-minute television commercials can the company have?

A) 12
B) 15
C) 20
D) 25

1 Answer

5 votes

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:

  1. The total amount spent on advertising is $97,000.
  2. The cost of a 1-minute radio commercial is $300.
  3. The cost of a 1-minute television commercial is $4,000.
  4. 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.

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