# Linear Inequalities Word Problems Goal Use linear inequalities

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: 5 x + 8 y ≥ 254

Word Problem 1 continued • 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: 2 x + 3 y ≤ 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 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: 4 x + 7 y ≥ 65

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