39. One online movie-streaming service costs $8 per month and charges $1.50 per movie. A second service costs $2 per month and charges $2 per movie. For what number of movies per month is the monthly cost of both services the same?
Answer: D
The monthly cost of both services is the same at 12 movies.
To find the number of movies per month where both services cost the same, we can set up an equation based on their pricing structures. For the first service, the total cost is represented as \(8 + 1.5m\), while for the second service, it is \(2 + 2m\). Setting these equal gives us the solution of 12 movies.
A) 3
Choosing 3 movies results in a cost of $8 + ($1.50 * 3) = $8 + $4.50 = $12. For the second service, the cost is $2 + ($2 * 3) = $2 + $6 = $8. Therefore, the costs are not equal at this quantity.
B) 6
At 6 movies, the cost for the first service is $8 + ($1.50 * 6) = $8 + $9 = $17. The second service costs $2 + ($2 * 6) = $2 + $12 = $14. The costs are still not equal at this quantity.
C) 5
With 5 movies, the first service costs $8 + ($1.50 * 5) = $8 + $7.50 = $15. The second service costs $2 + ($2 * 5) = $2 + $10 = $12. Again, the costs do not match at this number of movies.
D) 12
For 12 movies, the first service costs $8 + ($1.50 * 12) = $8 + $18 = $26. The second service costs $2 + ($2 * 12) = $2 + $24 = $26. This shows that both services cost $26 when 12 movies are rented, making this the correct answer.
E) 20
At 20 movies, the first service would cost $8 + ($1.50 * 20) = $8 + $30 = $38. The second service costs $2 + ($2 * 20) = $2 + $40 = $42. Hence, the costs are not equal at this quantity.
Conclusion
The analysis confirms that the monthly costs of both streaming services equalize at 12 movies. All other options either yield unequal costs or fall short of meeting the criteria for equivalence, reinforcing that option D is the only valid solution.