To determine how many movies a customer can watch while keeping the bill under \[tex]$60, we need to analyze the given pricing information for the cable TV service. Let's break down the steps:
1. Identify the flat fee: The flat fee for basic cable service is given as \$[/tex]25.
2. Determine the cost per movie: By examining the increases in the bill, we can see that:
- Watching 0 movies results in a bill of \[tex]$25.
- Watching 1 movie results in a bill of \$[/tex]29.
- Watching 2 movies results in a bill of \[tex]$33.
- Watching 3 movies results in a bill of \$[/tex]37.
From this information, we observe that each movie adds \[tex]$4 to the bill (since \$[/tex]29 - \[tex]$25 = \$[/tex]4, \[tex]$33 - \$[/tex]29 = \[tex]$4, and \$[/tex]37 - \[tex]$33 = \$[/tex]4).
3. Calculate the remaining amount available for movies: The total bill needs to be under \[tex]$60. Since the flat fee is \$[/tex]25, the remaining amount available for movies is:
[tex]\[
60 - 25 = 35
\][/tex]
4. Determine the maximum number of movies: Since each movie costs \[tex]$4, we need to figure out how many movies can be watched with the remaining \$[/tex]35. This can be done by dividing the remaining amount by the cost per movie:
[tex]\[
\frac{35}{4} = 8.75
\][/tex]
Because the number of movies watched must be a whole number, we take the integer part of this division, which is 8.
Thus, a customer can watch up to 8 movies and keep their cable bill under \[tex]$60. So, the maximum number of movies a customer can watch while keeping the bill under \$[/tex]60 is 8.
