Practice Graphing Linear Inequalities

Practice Problems

Now, let's practice putting all of our inequality knowledge to the test. Here are four problems for you to try. There are hints and videos if you need help working through them.

Noor wants to spend less than ‍$20 on condiments. Each kilogram of salt costs ‍$1.50, and each kilogram of pepper costs $2.50.

Write an inequality that represents the number of kilograms of salt $(S)$ and pepper ‍$(P)$ Noor can buy on her budget.
Jocelyn enjoys building robots and painting pictures. It takes her a constant amount of time to build every robot, and it takes her a constant amount of time to paint every picture. She has 15 hours to build robots and paint pictures.

In the following inequality, $R$ represents the number of robots Jocelyn can build and $P$ represents the number of paintings she can create over that time period:

$\qquad 2R+5P \leq 15$

Jocelyn wants to build 3 robots. How many paintings at most can she create in the time that remains?

Choose 1 answer:
1. Jocelyn can create at most 0 paintings.
2. Jocelyn can create at most 1 painting.
4. Jocelyn can create at most 2 paintings.
5. Jocelyn can create at most 3 paintings.
Goku wants to get over 9000 comments on his YouTube videos. He gets the same number of comments for each cat video that he uploads, and he gets the same number of comments for each dog video that he uploads.

Let $C$ represent the number of cat videos and $D$ represent the number of dog videos that Goku should upload to achieve his goal.

$750C+450D > 9000$

According to the inequality, how many comments does each cat video get, and how many comments does each dog video get?

Each cat video gets ___ comments, and each dog video gets ___ comments.

Can Goku achieve his goal by uploading 8 cat videos and 7 dog videos?

Choose 1 answer:
1. Yes
2. No
Miyoko's goal is to earn more than ‍$950 this week. She earns $250 for every day she works as a cryptographer, and earns $180 for every day she works as a geologist.

Write an inequality that represents the number of days Miyoko should work as a cryptographer $C$ and as a geologist ‍$G$ to achieve her goal.

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:modeling-with-linear-inequalities/e/modeling-constraints
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