Mastering Linear Inequalities and Systems for 9th Grade

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write a system of inequalities to represent the number of students that can attend the trip. How many students can they take?

• 20

• 14

• 10

• 5

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. If the company has 30 hours of labor available, write an inequality to represent the production limits. How many of each gadget can they produce?

• The company can produce a maximum of 12 gadgets A (0 gadgets B) or 8 gadgets B (0 gadgets A).

• The company can produce a maximum of 15 gadgets A (0 gadgets B) or 10 gadgets B (0 gadgets A), or any combination that satisfies 2x + 3y ≤ 30.

• The company can produce a maximum of 20 gadgets A (0 gadgets B) or 5 gadgets B (0 gadgets A).

• The inequality representing production limits is 2x + 2y ≤ 30.

A concert venue can hold a maximum of 200 people. If tickets for adults cost $15 and tickets for children cost $10, write an inequality to represent the total revenue generated if the venue is at full capacity. What are the possible combinations of adult and child tickets sold?

• x + y < 200

• x + y ≤ 200, where x is the number of adult tickets and y is the number of child tickets.

• x + y ≥ 200

• x + y = 200

A local bakery sells muffins and cookies. Each muffin costs $2 and each cookie costs $1. If the bakery wants to make at least $100 in sales, write an inequality to represent the relationship between the number of muffins (m) and cookies (c) sold. What are the possible combinations of muffins and cookies?

• m + c >= 50

• 3m + c <= 100

• 2m + c >= 100

• m + 2c >= 100

A gym has a maximum capacity of 50 members. If 30 members are currently enrolled, write an inequality to represent the number of new members (n) that can join. How many new members can the gym accept?

• 15

• 25

• 10

• 20

A charity event aims to raise at least $1,000. If each ticket sold is $25 and each donation is $50, write an inequality to represent the relationship between the number of tickets (t) sold and donations (d) received. What are the possible combinations of tickets and donations?

• 50t + 25d >= 1000

• 25t + 50d = 1000

• 25t + 50d >= 1000

• 25t + 50d <= 1000

A restaurant has a special offer where a meal costs $12 and a drink costs $3. If a customer wants to spend no more than $60, write an inequality to represent the number of meals (m) and drinks (d) they can purchase. What are the possible combinations?

• 10m + 5d ≤ 60

• 12m + 4d ≤ 60

• 12m + 3d ≤ 60

• 15m + 2d ≤ 60

A student is saving money for a new laptop that costs $800. If they save $50 a week from their allowance, write an inequality to represent the number of weeks (w) it will take to save enough money. How many weeks will it take?

• 16 weeks

• 20 weeks

• 12 weeks

• 10 weeks

A clothing store has a sale where shirts cost $20 and pants cost $30. If a customer wants to spend no more than $150, write an inequality to represent the number of shirts (s) and pants (p) they can buy. What are the possible combinations of shirts and pants?

• 20s + 30p < 150

• 20s + 30p ≤ 150

• 10s + 20p ≤ 150

• 20s + 30p = 150