To determine which company charges more for renting 15 movies, we need to analyze the cost patterns for each company based on the provided data.
Step-by-step solution:
1. Identify the cost pattern for Movies Plus:
- For 0 movies: [tex]\(\$10\)[/tex]
- For 2 movies: [tex]\(\$14\)[/tex] (an increase of [tex]\(\$4\)[/tex])
- For 4 movies: [tex]\(\$18\)[/tex] (an increase of [tex]\(\$4\)[/tex])
- For 10 movies: [tex]\(\$30\)[/tex] (an increase of [tex]\(\$12\)[/tex] over 6 movies)
From the data, we can see the increase pattern:
- The cost increases by [tex]\(\$4\)[/tex] for every 2 movies rented from 0 to 4 movies.
- From 4 to 10 movies, the cost increases by [tex]\(\$12\)[/tex] over 6 movies, which corresponds to [tex]\(\$2\)[/tex] per additional movie.
2. Extrapolate the cost for Movies Plus beyond 10 movies:
- For the next 5 movies (from 10 to 15 movies), continue the same pattern of [tex]\(\$2\)[/tex] per movie.
- Cost for 15 movies = Cost for 10 movies + (5 movies [tex]\(\times \$2/\text{movie}\)[/tex])
- Cost for 15 movies = [tex]\(\$30 + (5 \times 2) = \$30 + \$10 = \$40\)[/tex]
3. Identify and extrapolate the cost pattern for Movies For Less:
- For 0 movies: [tex]\(\$0\)[/tex]
- For 2 movies: [tex]\(\$6\)[/tex] (an increase of [tex]\(\$6\)[/tex])
- For 4 movies: [tex]\(\$12\)[/tex] (an increase of [tex]\(\$6\)[/tex])
From the data, we can see Movies For Less charges a linear rate of [tex]\(\$3\)[/tex] per movie rented.
4. Calculate the cost for Movies For Less for 15 movies:
- Cost per movie = [tex]\(\$3\)[/tex]
- Cost for 15 movies = [tex]\(15 \times 3 = \$45\)[/tex]
5. Compare the total costs:
- Movies Plus for 15 movies: [tex]\(\$40\)[/tex]
- Movies For Less for 15 movies: [tex]\(\$45\)[/tex]
6. Determine the difference in costs:
- Difference = Movies For Less cost - Movies Plus cost
- Difference = \[tex]$45 - \$[/tex]40 = \[tex]$5
Thus, Movies For Less costs \(\$[/tex]5\) more than Movies Plus when renting 15 movies.
Conclusion:
The statement that is true is:
- Movies For Less costs \$5 more.
