Representing Inequalities in Word Problems

Systems of Linear Inequalities

Word Problems

Use a system of linear inequalities to model a real-life situation.

​Word Problems

• Most of these problems will not give you a slope and y

  intercept.

• You will not be writing inequalities in slope-intercept form.

• You will be writing equations in standard form.

Standard Form Word Problems

• Figure out what x and y represent

• Write an inequality for each topic in the topic

​Word Problem #1

You can work a total of no more then 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.

​Word Problem #2

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write and graph a system of linear inequalities to represent this situation.

​Word Problem #3

A salad contains ham and chicken. There are at most 6 pounds of ham and chicken in the salad. Write and graph a system of inequalities to represent this situation.

​Word Problem #4

Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write and graph a system of inequalities to represent this situation.

Multiple Choice

What's the difference between systems of equations and systems of inequalities?

• Systems of equations have 1 solution, no solution, or infinite solutions while systems of inequalities can have a range of solutions.

• Systems of equations use slope-intercept form only while systems of inequalities use standard form only.

• Systems of equations have a shaded region while systems of inequalities do not.

• There is no difference.

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5 x+y=87

• 1.5x+0.5y=78.5 1.5x+0.5y=87

• x+y=78.5 1.5x+0.5y=87

• x+y=78.5 x+y=87

Multiple Choice

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

• x + y ≥ 6 32x + 20y ≤ 150

• x + y ≥ 632 x + 20y ≥ 150

• x + y ≤ 6 32x + 20y ≤ 150

• x + y ≤ 6 32x + 20y ≥ 150

Multiple Choice

Ross and Chandler go to Taco Land and order sodas for a total of $3.50. They also want to order some tacos (of course), which cost $1.75 each. If they have $20, how many tacos can they buy? Which inequality best represents the situation.

• 3.50 + 1.75t > 20

• 1.75 + 3.50t ≤ 20

• 3.50 + 1.75t ≥ 20

• 1.75t + 3.50 ≤ 20