Publish on 27th October 2019
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7.6 Systems of Linear Inequalities Word Problems

Goal: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 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 = housecleaningy = sales jobHours: x + y ≤ 41Money: 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 xy = fuel yPrice: 2x + 3y ≤ 18Gallons of x: x ≥0Gallons 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 = hamy = chickenTotal Pounds: x + y ≤ 6Pounds of ham: x ≥ 0Pounds 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 = babysittingy = tutoringHours: x + y ≤ 13Money: 4x + 7y ≥ 65

Practice

Worksheet – “System of Linear Inequalities Word Problems”

Homework

Worksheet – “System of Linear Inequalities Word Problems Homework”

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7.6 Systems of Linear Inequalities Word Problems