Systems of Linear Inequalities Word Problems Objective: 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. Write an inequality for each topic in the problem.

Word Problem #1 Write an inequality for each topic (Hours AND $$) You can work no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job. h = housecleaning AND s = sales job Write an inequality for each topic (Hours AND $$) Hours: h + s ≤ 41 Money: 5h + 8s ≥ 254

Let’s make tables so that we can graph the inequalities Hours: h + s ≤ 41 When h is 0, s is? ___ When s is 0, h is? ___ Money: 5h + 8s ≥ 254 It’s easiest to find the x and y intercepts and graph those Housecleaning (X) Sales job (Y) Housecleaning (X) Sales job (Y)

Word Problem #2 Jonah needs to buy at least 20 candles for teacher and staff appreciation gifts. The small candles cost $3.50 and the large candles cost $5.00. He has at most $80.00 to spend. Write a system of linear inequalities to represent this situation. s = small candles l = large candles Write an inequality for each topic Price: 3.5s + 5l ≤ 80 Number of candles: s + l ≥ 20

Price: 3.5s + 5l ≤ 80 Number: s + l ≥ 20 Let’s make tables so that we can graph the inequalities Price: 3.5s + 5l ≤ 80 When s is 0, l is? ___ When l is 0, s is? ___ Number: s + l ≥ 20 When s is l, s is? ___ (When you buy o small candles, how many large can you buy?) It’s easiest to find the x and y intercepts and graph those Small (X) Large (Y) Small (X) Large (Y)

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 because she needs to focus on her school work. She wants to make at least $65 a week. Write and graph a system of inequalities to represent this situation. b = babysitting t = tutoring Hours: b + t ≤ 13 Money: 4b + 7t ≥ 65

Homework Worksheet – “4.1 Systems of Inequalities”