Inequalities in Action: Graphing & Word Problem Translation

1. Sarah has $50 to spend on school supplies. If she buys notebooks for $3 each and pens for $2 each, how many notebooks and pens can she buy if she wants to spend less than $50? Write an inequality and graph it on a number line.

• (15 notebooks, 0 pens)

• (5 notebooks, 20 pens)

• Sarah can buy various combinations of notebooks and pens as long as 3x + 2y < 50, for example, (0 notebooks, 25 pens), (10 notebooks, 5 pens), etc.

• (25 notebooks, 0 pens)

2. A movie theater charges $10 for adult tickets and $7 for child tickets. If a family wants to spend no more than $50 on tickets, how many adult and child tickets can they buy? Set up an inequality and solve it.

• (3 adult, 4 child)

• (2 adult, 6 child)

• (0 adult, 10 child)

• The family can buy combinations of tickets such as (0 adult, 7 child), (1 adult, 5 child), (2 adult, 3 child), (3 adult, 1 child), (4 adult, 0 child), or (5 adult, 0 child).

3. A gardener has 120 feet of fencing to create a rectangular garden. If the length of the garden must be at least 10 feet longer than the width, what are the possible dimensions of the garden? Write and solve the inequality.

• Width: 25 feet, Length: 35 feet

• Width: 30 feet, Length: 40 feet

• Width: 15 feet, Length: 25 feet

• Width: 20 feet, Length: 30 feet

4. A store is having a sale where each shirt costs $15 and each pair of pants costs $25. If a customer wants to buy at least 3 shirts and spend no more than $100, what is the maximum number of pants they can buy? Formulate the inequality and solve it.

• 2

• 3

• 1

• 4

5. Jamie is saving money to buy a new bike that costs $200. If she saves $20 each week, how many weeks will it take her to save enough money? Write an inequality to represent this situation and solve it.

• 10 weeks

• 5 weeks

• 15 weeks

• 20 weeks

6. A school is planning a field trip and has a budget of $300. If each student ticket costs $15 and they want to take at least 10 students, how many additional students can they take without exceeding the budget? Create and solve the inequality.

• 20

• 10

• 15

• 5

7. A recipe requires at least 2 cups of flour and 1 cup of sugar. If each cup of flour costs $2 and each cup of sugar costs $3, how much can you spend on flour and sugar if you want to keep the total cost under $20? Write the inequality and graph it.

• 2x + 3y < 20, x >= 2, y >= 1

• 2x + 3y < 15, x >= 1, y >= 2

• 2x + 3y > 20, x >= 3, y >= 1

• 2x + 3y = 20, x >= 2, y >= 0

8. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $50, how many miles can they drive? Set up the inequality and solve it.

• 80 miles

• 120 miles

• 60 miles

• 100 miles

9. A student needs to score at least 75% on their final exam to pass the class. If the exam is worth 100 points and they have already scored 60 points on the first part, what score do they need on the second part? Write the inequality and solve it.

• 20

• 15

• 30

• 10

10. A fitness center offers a monthly membership for $40 and charges $5 per class. If a member wants to spend no more than $100 in a month, how many classes can they attend? Formulate the inequality and solve it.

• 8

• 20

• 15

• 12