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?

Rationale

For 12 movies per month, the monthly cost of both services is the same.

When calculating the total cost for each streaming service based on the number of movies rented, both services equate at a total monthly cost of $26 when 12 movies are streamed. This demonstrates the point at which their costs intersect.

A (3) YOUR ANSWER

For 3 movies, the first service costs $8 + ($1.50 × 3) = $8 + $4.50 = $12.50, while the second service costs $2 + ($2 × 3) = $2 + $6 = $8. Thus, the costs are not equal at this level of movie rentals.

B (6) YOUR ANSWER

At 6 movies, the first service totals $8 + ($1.50 × 6) = $8 + $9 = $17, while the second service totals $2 + ($2 × 6) = $2 + $12 = $14. The costs are still not equal at this number of movies.

C (5) YOUR ANSWER

For 5 movies, the first service totals $8 + ($1.50 × 5) = $8 + $7.50 = $15.50, and the second service totals $2 + ($2 × 5) = $2 + $10 = $12.50. Again, the costs do not match at this point.

D (12) CORRECT

When renting 12 movies, the first service costs $8 + ($1.50 × 12) = $8 + $18 = $26, while the second service costs $2 + ($2 × 12) = $2 + $24 = $26. Thus, both services cost the same at 12 movies.

E (20) YOUR ANSWER

At 20 movies, the first service costs $8 + ($1.50 × 20) = $8 + $30 = $38, while the second service costs $2 + ($2 × 20) = $2 + $40 = $42. The costs diverge further at this number of rentals.

Conclusion

The intersection point of costs for the two movie-streaming services occurs at 12 movies, where both services charge $26. This analysis demonstrates the significance of comparing fixed fees alongside variable costs to identify break-even points in service pricing. Thus, understanding these calculations can guide consumers in selecting the most economical option based on their anticipated usage.