7.6 Systems of Linear Inequalities Word Problems Use a system of linear inequalities to model a real-life situation.

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7.6 Systems of Linear Inequalities Word Problems

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Presentation transcript:

7.6 Systems of Linear Inequalities Word Problems Use a system of linear inequalities to model a real-life situation.

Reminders!!!

Homework Questions? ?!?!?!

Quick Application Video dJ8o dJ8o

Standard Form of Word Problems Define variables Write out the system Graph the inequalities Write 2 possible solutions

Word Problem #1 You can work a total of no more than 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 hours y = sales job hours 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 = gallons of fuel x y = gallons of fuel y Price:2x + 3y ≤ 18 Gallons of x:x ≥0 Gallons of y: y ≥ 0

Word Problem #2 Graphing… Price:2x + 3y ≤ 18 Gallons of x:x ≥0 Gallons of y: y ≥ 0 Think about your intercepts when graphing the first inequality

Word Problem #2 Graphing… Price:2x + 3y ≤ 18 Gallons of x:x ≥0 Gallons of y: y ≥ 0 The shaded region are All the possible solutions That satisfy each inequality Possible answers ( 1,1) (2, 4) (0,6)

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 = lbs of ham y = lbs of chicken Total Pounds: x + y ≤ 6 Pounds of ham:x ≥ 0 Pounds of chicken: y ≥ 0

Word Problem #3 Graphing… Total Pounds: x + y ≤ 6 Pounds of ham:x ≥ 0 Pounds of chicken: y ≥ 0 Remember we cannot have negative lbs!! Possible solutions 1 lb of ham and 1 lb of chicken 3 lbs of ham and 2lbs of chicken

Word Problem #4

Possible Solutions 2 hours babysitting and 9 hours tutoring 1 hour babysitting and 10 hours tutoring

7.6 Practice Worksheet You may work with your partner or work independently on this.

7.5/7.6 Exit Card This will be graded Answer each question as best as you can If you finish early, on the back of the page write down and questions you have about the current topic