Systems of Inequalities Word Problems

Inequalities Word Problems

Solving One & Two Step Inequalities from Word Problems

When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:

Fill in the Blanks

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Multiple Choice

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

Which of the following inequalities would correctly represent the required length of the post?

• 
  

  $$x\ \ge\ 5$$

• $$x\ \le\ 5$$

• $$x\ -\ 3\ \ge\ 5$$

• $$x\ +\ 3\le\ 5$$

Fill in the Blanks

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Poll

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left? 

What inequality symbol would you be using to solve this problem? (Assume your variable comes first.)

• >

• <

• $$\le$$  

• $$\ge$$  

Multiple Choice

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

Which inequality would help you solve this problem correctly?

• $$x\ +\ 14\ \le\ 35$$

• $$x\ +\ 14\ \ge35$$

• $$x\ -\ 14\ \ge35$$

• $$x\ -\ 14\ \le\ 35$$

Poll

Each gumball in a gumball machine costs $0.25. You can spend no more than $2.50 in total on gumballs.

What inequality symbol would you use to represent this problem? (Assume the variable is on the left.)

• >

• <

• $$\ge$$  

• $$\le$$  

Multiple Choice

Each gumball in a gumball machine costs $0.25. You can spend no more than $2.50 in total on gumballs.

Which inequality would represent how many gumballs you could buy?

• $$0.25x\ <\ 2.50$$

• $$0.25x\ >\ 2.50$$

• $$0.25x\ \le\ 2.50$$

• $$0.25x\ \ge\ 2.50$$

Multiple Choice

You have $30 to buy baseball cards. Each pack of cards costs $5. Write an inequality that represents the number of packs of baseball cards you can buy and still have at least $10 left.

• $$30\ -\ 5x\ \ge10$$

• $$30\ -\ 5x\ \le\ 10$$

• $$30\ -\ 5x\ <\ 10$$

• $$30\ -\ 5x\ >\ 10$$

Multiple Choice

You borrow $200 from a friend to help pay for a new laptop computer. You pay your friend back $12 per week. Write and solve an inequality to find when you will owe your friend less than $56.

Which one of the following inequalities would be the correct answer?

• x < 12

• x > 12

• x < 21

• x > 21

Multiple Choice

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 200 + 25x ≥ 500

• 500 + 25x ≥ 200

• 500 - 25x ≥ 200

• 500 - 25x ≤ 200

Multiple Choice

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Multiple Choice

Last Friday Samantha had $22.50. Over the weekend, she received some money for cleaning. She now has more than $32.00. Which inequality represents this situation?

• 22.50 - x > 32

• 22.50x > 32

• 22.50 + x > 32

• 22.50 +x < 32

Multiple Choice

The girls’ swim team is hosting a fund raiser. They would like to raise at least $500. They are selling candles for $5 and flower arrangements for $6. The girls estimate that at most they will sell 200 items.

Which answer represents the system?

• $$5C+6F>500\ \$$ $$C+F<200$$

• $$5C+6F\ge200$$ $$C+F\le500$$

• $$5C+6F\ge500$$ $$C+F\le200$$

• $$6C+5F\le500$$ $$6C+5F\ge200$$

Multiple Choice

The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door.

• $$3A+4D>300$$ $$A+D<500$$

• $$3A+4D\ge500$$ $$A+D\le300$$

• $$4A+3D\ge500$$ $$A+D<300$$

• $$3A+4D<300$$ $$A+D>500$$

Multiple Choice

Jenny is making jewelry for an Arts and Crafts show. She would like to make a minimum of $100 in sales. She estimates that she will sell no more than 50 pieces of jewelry. The bracelets that she is selling cost $2 and the necklaces cost $3.

• $$3B+2N>100$$ $$B+N<50$$

• $$2B+3N\ge100$$ $$B+N\le50$$

• $$2B+3N\ge50$$ $$B+N\le100$$

• $$2B+3N\ge100$$ $$2B+3N\le50$$

Multiple Choice

In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have less than $30 to spend. You expect to purchase more than 3 pounds of hamburgers and chicken.

Write a system of inequalities.

• $$2H+3C>30$$ $$H+C<3$$

• $$3H+2C<30$$

  $$H+C>3$$

• $$2H+3C\le30$$

  $$H+C\ge3$$

• $$2H+3C<30$$

  $$H+C>3$$

Multiple Choice

You need at least 3 lbs of fruit to make muffins.

Blueberries are $4 per lb and strawberries are $5 per lb. You can spend at most $20 on fruit. Write a system of inequalities.

• $$4B+5S\le20$$

  $$B+S\ge3$$

• $$4B+5S\ge20$$

  $$B+S\le3$$

• $$5B+4S<20$$

  $$B+S>3$$

• $$5B+4S\ge3$$

  $$B+S\le20$$