Linear Inequalities Word Problems Goal: Use 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 need to write the equations in Slope- Intercept Form.

Word Problem #1 Mary works 2 jobs to make enough money to pay her bills. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 to pay your bills. Write a linear inequality that shows the various numbers of hours you can work at each job. x = housecleaning y = sales job Money: 5x + 8y ≥ 254

Word Problem 1continued If Mary work 3 hours at the house cleaning job, what is the minimum amount of hours you must work to make $254.00? If Mary work 8 hours at the house cleaning job, and 12 hours at the sales job, will she be able to pay her bills?

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 linear inequality to represent this situation. x = fuel x y = fuel y Price: 2x + 3y ≤ 18

If you fill your car with 9 gallons of fuel x, how many gallons can you buy of fuel x? Create a situation that would be a false solution.

Word Problem #3 A salad at a deli 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. x = ham y = chicken Total Pounds: x + y ≤ 6

When you go to the deli, can you buy partial pounds of sliced meat? If you buy 3.4 pounds of ham, how much turkey would you need to buy to surpass your 6 pound limit?

Word Problem #4 Elizabeth babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65. Write and graph a linear inequality to represent this situation. x = babysitting hours y = tutoring hours Money: 4x + 7y ≥ 65