Question

You give a gift card worth $90. You want to buy several movies that cost $12 each. Write and solve an inequality that represents the number of movies you can buy and still have at least $30 on the gift card.

Answer 1

Hello! We can write and solve an inequality like this:

90 - 12n ≥ 30

We set it up like this, because you have $90 on your gift card. It is $12 per movie, and you want to have at least $30 left, which means the symbol will be the greater than or equal to symbol (≥), because you want to have at least $30 or more remaining. Having exactly $30 left also counts in this equation.

How to solve the inequality:

First off, subtract 90 from both sides in order to get -12n ≥ - 60. Now, divide each side by -12 to isolate the "n". Because you are dividing a negative by a negative, your answer will be positive. -60/-12 is 5. Let's check it. 12 * 5 is 60. 90 - 60 is 30. 30 ≥ 30. And you divided by a negative, so we change the symbol to the less than or equal to sign (≤). There. n ≤ 5.