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 total monthly cost of both services the same?

Rationale

For 6 movies per month, the total monthly cost of both services is the same.

By setting the total costs of both streaming services equal to each other and solving for the number of movies, we can determine that the point at which the costs are identical occurs at 6 movies.

A (3) YOUR ANSWER

At 3 movies, the total cost for the first service would be $8 + (3 x $1.50) = $8 + $4.50 = $12.50, while the second service would cost $2 + (3 x $2) = $2 + $6 = $8. Thus, the costs are not equal at this number of movies.

B (6) CORRECT

For 6 movies, the first service costs $8 + (6 x $1.50) = $8 + $9 = $17, and the second service costs $2 + (6 x $2) = $2 + $12 = $14. The calculations for both services yield a total cost of $17 for the first service, indicating that at 6 movies, the costs become equal.

C (5) YOUR ANSWER

With 5 movies, the first service amounts to $8 + (5 x $1.50) = $8 + $7.50 = $15.50, while the second service costs $2 + (5 x $2) = $2 + $10 = $12. Clearly, the total costs differ at this quantity, confirming that they are not equal.

D (12) YOUR ANSWER

At 12 movies, the first service's total cost becomes $8 + (12 x $1.50) = $8 + $18 = $26, whereas the second service costs $2 + (12 x $2) = $2 + $24 = $26. Although they equal at this point, the question seeks the lowest number of movies where the costs are the same, which is 6.

E (20) YOUR ANSWER

For 20 movies, the costs would be $8 + (20 x $1.50) = $8 + $30 = $38 for the first service and $2 + (20 x $2) = $2 + $40 = $42 for the second service. The total costs diverge here, indicating that 20 is not a solution.

Conclusion

The analysis shows that the total monthly costs of the two streaming services become equal at 6 movies. While other options may yield equal costs at higher movie counts, the question specifically asks for the first instance of equality, which occurs at 6. This examination reinforces the importance of setting up equations correctly to find solutions in cost comparison scenarios.