Name: _________________________________ Date: __________________

AU4: Notes #6 – Linear Inequality Word Problems

1. Suppose your class is raising money for the Red Cross. You make $3 on each basket of fruit and $5 on each box of cheese that you sell. How many items of each type must you sell to raise more than $100?


2. JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?


3. Math Club members want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. They have a $30 advertising budget. It cost $2 for each front-page ad and $1 for each inside-page ad. The club wants to advertise at least 20 times.

a) Write and graph a system of inequalities to model the number of advertisements the club can purchase to stay under budget. Be sure to label all parts of your graph.

b) State one solution that would work. How much money will remain in the club’s budget?

Name: _________________________________ Date: ________________

AU4: HW #6 – Linear Inequality Word Problems

1. Suppose you intend to spend no more than $60 buying books. Hardcover books cost $12 and paperback cost $5. How many books of each type can you buy?


2. Miss Jones wants to buy at least 10 books. Each paperback book costs an average of $10 and each hardcover book costs an average of $20. Miss Jones is planning to spend less than $240 on books.

c) Write and graph a system of inequalities to model the number of books she can purchase to stay under budget. Be sure to label all parts of your graph.

d) State one solution that would work. How much did she spend on hardcover books?


3. The science club wants to buy t-shirts for the organization. They have a budget of $120. Plain white t-shirts cost $3 and red t-shirts with writing costs $6. There are 20 students in the club but all are not sure if they are going to purchase a t-shirt.

a) Write and graph a system of inequalities to model the number of t-shirts the club can purchase to stay under budget.

b) State one solution that would work. How many more white t-shirts could they buy? Explain.

Name: ______________________ Class: __________________

AU4: Systems of Equations Unit Review Total: 42 pts

What is the solution set to the following system of linear equations?

If there is no solution or infinitely many, explain why. (3pts each)

#1.

#2.

Solve the following systems of equations algebraically.

Show all work and check only #3. (4 pts each)

#3. Check:

#4. #5.

#6. Suppose you bought supplies for a party. Three rolls of streamers and fifteen party hats cost $30. Later, you bought two rolls of streamers and four party hats for $11. Write and solve a system of equations to determine the cost of streamers and party hats, find their costs. (4 pts)

#7. John flies from Atlanta, GA to San Francisco, CA. It takes 5.6 hours to travel 2,100 miles against the head winds. At the same time, Debbie flies from San Francisco to Atlanta. Her plane travels with the same average airspeed but with a tailwind her flight only takes 4.8 hours. Write and solve a system of equations to determine the air speed of the plane and the wind speed. (4 pts)

#8. Sam needs to rent a car for a one-week trip to Oregon. He is considering two companies:

A+ Auto Rental: $175 plus $0.10 per mile

Zippy Auto Rental: $220 plus $0.05 per mile.

Write and solve a system of equations to determine when the rental costs are the same for both companies. (3pts)


Write a system of linear inequalities for the graph shown below.

#9. (3 pts)

Solve the system of linear inequalities by graphing. (4 pts)

#10.


#11. You have a gift certificate to a book store worth $60. Each paperback book is $4 and each hardcover book is $15. You must buy at least 5 books in order to use the gift certificate.

(6 pts)

e) Write and graph a system of inequalities to model the number of each kind of books you can buy. Be sure to label all parts of your graph.

f) State one solution that would work, and determine how much money remains on your gift certificate.


4 pt Bonus:

11