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We are given:

- In 1985, there were 12.4 million households with cable TV and 26.8 million households with magazine subscriptions.
- The number of cable TV households increases by 1.2 million per year.
- The number of magazine subscriptions decreases by 2.4 million per year.

We need to find how many years it will take for the number of households with cable TV to equal the number of households with magazine subscriptions.

Let \( t \) represent the number of years after 1985.

- The number of cable TV households after \( t \) years will be:
  \[
  12.4 + 1.2t
  \]
  
- The number of magazine subscription households after \( t \) years will be:
  \[
  26.8 - 2.4t
  \]

To find when these two are equal, we set the equations equal to each other:
\[
12.4 + 1.2t = 26.8 - 2.4t
\]

Now, solving for \( t \):

\[
12.4 + 1.2t = 26.8 - 2.4t
\]
\[
1.2t + 2.4t = 26.8 - 12.4
\]
\[
3.6t = 14.4
\]
\[
t = \frac{14.4}{3.6} = 4
\]

Thus, it will take **4 years** for the number of cable TV households to equal the number of magazine subscriptions.

The correct answer is **C) 4 years**.

Would you like more details or have any questions? Here are some related questions to further explore:

1. What happens if the increase in cable TV households changes over time?
2. How would the equation change if the magazine subscriptions decreased at a different rate?
3. What would happen if both cable TV and magazine subscriptions followed exponential growth/decay?
4. Can you calculate how many households will have cable TV after 10 years?
5. How many households will have magazine subscriptions after 5 years?

**Tip:** Always remember to set up equations carefully to model changing rates when solving word problems like this one.

In 1985, 12.4 million households had cable TV and 26.8 million households had magazine subscriptions. Since then, the number of households with cable TV had increased by 1.2 million households per year while magazine subscriptions decreased by 2.4 million households per year. How many years would it take for the number of households with cable TV to equal the number of households with magazine subscriptions?

Learn how to solve a word problem involving linear equations. In this problem, households with cable TV increase while magazine subscriptions decrease, and we calculate when the two numbers will be equal. Suitable for Grades 6-8.

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