Question

You have $370. You find a DVD player that costs $257. New release movies cost $21 and older release movies cost $14. Write and solve an inequality to find the number of movies you can buy for your new DVD player if you buy an equal number of old and new movies.

Answer 1

you can buy at most 10 movies for your new DVD player if you buy an equal number of old and new movies, without exceeding your budget of $370

Explanation:

Let's use the variable "x" to represent the number of movies (both old and new) you can buy. Since you have $370 and each new release movie costs $21 and each older release movie costs $14, the total cost of the movies can be expressed as:

Total cost of movies = (Number of new movies + Number of old movies) × (Cost per new movie + Cost per old movie)

So, we have:

Total cost of movies = x × (21 + 14)

Now, you want to ensure that the total cost of the movies you buy doesn't exceed the amount of money you have, which is $370. Therefore, you can write the following inequality:

x × (21 + 14) ≤ 370

Simplify the inequality:

x × 35 ≤ 370

Now, to solve for "x," divide both sides of the inequality by 35:

x ≤ 370 / 35

x ≤ 10.57 (rounded to two decimal places)