# 7.6 Systems of Linear Inequalities Word Problems Goal: Use a system of

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7.6 Systems of Linear Inequalities Word Problems Goal: Use a system of linear inequalities to model a reallife 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 problem.

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. x housecleaning y sales job Hours: x y 41 Money: 5x 8y 254

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. x fuel x y fuel y Price: 2x 3y 18 Gallons of x: x 0 Gallons of y: y 0

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. x ham y chicken Total Pounds: x y 6 Pounds of ham: x 0 Pounds of chicken: y 0

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. x babysitting y tutoring Hours: x y 13 Money: 4x 7y 65

Practice Worksheet – “System of Linear Inequalities Word Problems”

Homework Worksheet – “System of Linear Inequalities Word Problems Homework”