Algebra Name: ______
Systems of Linear Inequalities
Interpreting Solutions to Problems
Complete the following.
1. Trevor always leaves a tip of between 7% and 22% for the server when he pays for dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip, and x is the cost of dinner.
y > 0.07x
y < 0.22x
Which of the following is a true statement?
A. When the cost of dinner (x) is $15, the amount of tip (y) must be between $3.30 and $10.50.
B. When the cost of dinner (x) is $30, the amount of tip (y) must be between $2.10 and $6.60.
C. When the amount of tip (y) is $7, the cost of dinner (x) must be between $10 and $31.
D. When the amount of tip (y) is $1.32, the cost of dinner (x) must be between $6 and $13.
2. Tony wants to plant at least 40 acres of corn. He wants at least 200 acres of corn and soybeans. This can be represented by the system of inequalities shown below, where x represents the number of acres of soybeans, and y represents the number of acres of corn.
x + y 200
y 40
Which of the following is a true statement?
A. When Tom plants 50 acres of corn, the acres of soybeans must be between 100 and 150.
B. When Tom plants 75 acres of corn, the acres of soybeans must be between 40 and 125.
C. When Tom plants 65 acres of corn, the acres of soybeans must be at least 135.
D. When Tom plants 40 acres of corn, the acres of soybeans must be at least 140.
3. Gloria is starting her own company making teddy bears. She has enough bear bodies to create 40 bears. She will make girl and boy teddy bears. Gloria will charge $15 for girl bears and $12 for boy bears. She wants to earn at least $540 a week. This can be represented by the system of inequalities shown below, where y represents the number of girl teddy bears, and x represents the number of boy teddy bears.
x + y 40
12x + 15y 540
Using the graph, which of the following statements is true?
A. Gloria would make the most money selling 20 boy and 20 girl teddy bears.
B. Gloria would make the most money selling 40 girl teddy bears and no boy teddy bears.
C. Gloria must sell at least 36 girl teddy bears to reach her weekly income goal.
D. Gloria must sell at least 40 boy teddy bears to reach her weekly income goal.
4. Sal’s Surf Shop makes $150 profit for every surfboard sold and $100 profit for every wakeboard sold. Sal sells at least 15 total boards each month and he wants to earn at least $2000 a month. This can be represented by the system of inequalities shown below, where x represents the number of surfboards sold, and y represents the number of wakeboards sold.
x + y 15
150x + 100y 2000
Using the graph, what does the solution represent?
A. The number of surfboards and wakeboards Sal must sell to break even.
B. The number of surfboards and wakeboards Sal must sell to make $2000.
C. The number of surfboards Sal must sell to make $2000.
D. The number of wakeboards Sal must sell to make $2000.
5. At her party, Alice is serving pepper jack and cheddar cheese. She wants to have at least 3 pounds total. Alice wants to spend at most $20 on cheese. The pepper jack cheese is $4 per pound and the cheddar cheese is $2 per pound. Let x represents the number of pounds of pepper jack cheese, and y represents the number of pounds of cheddar cheese. Write a system of inequalities and graph the solution set.
System of Inequalities:
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6. Strayer’s 8th grade class is raising money for the American Red Cross and wants to advertise in the local newspaper. We have a $30 advertising budget. It costs $2 for each front-page ad and $1 for each inside-page ad. We were hoping to advertise at least 20 times in the newspaper. Let x represents the number front page ads, and y is the number of inside-page ads. Write a system of inequalities and graph the solution set.
System of Inequalities:
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7. Lucas intends on spending less than $60 on new books. Hardback books cost $10 and paperback books cost $5. Lucas’ mom told him he must purchase at least 4 books total. Let x represents the number of paperback books, and y represents the number of hardback books. Write a system of inequalities and graph the solution set.
System of Inequalities:
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8. Selena is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and earrings cost $3. She needs to make at least $300. Selena knows she will sell more than 50 bracelets. Let x is the number of bracelets sold, and y is the number of earrings sold. Write a system of inequalities and graph the solution set.
System of Inequalities:
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9. 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 cost $6. There are 20 students in the club but not all are sure if they are going to purchase a t-shirt. Let x is the number of white t-shirts purchased, and y is the number of red t-shirts with writing purchased. Write a system of inequalities and graph the solution set.
System of Inequalities:
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10. Jason is buying wings and hot dogs for a party. One package of wings cost $8. Hot dogs cost $4 per pound. He knows he must be at least 5 pounds of hot dogs and he has to spend less than $40. Let x is the number of packages of wings purchased, and y is the number of pounds of hot dogs purchased. Write a system of inequalities and graph the solution set.
System of Inequalities:
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