Inequalities in Action: Combine & Validate Solutions

1. Sarah has $50 to spend on school supplies. She wants to buy notebooks for $3 each and pens for $2 each. If she buys x notebooks and y pens, write an inequality to represent her budget. Combine like terms and solve for the maximum number of notebooks she can buy if she buys 5 pens.

• 10

• 12

• 13

• 15

2. A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality to represent the number of classes (c) they can attend. Combine like terms and find the maximum number of classes they can take.

• 12

• 16

• 10

• 14

3. A concert hall has a seating capacity of 500. If tickets are sold for $20 each and the hall wants to make at least $8,000, write an inequality to represent the number of tickets (t) that must be sold. Combine like terms and determine the minimum number of tickets that need to be sold.

• 300

• 350

• 450

• 400

4. Emily is saving money for a new bike that costs $200. She saves $15 each week and has already saved $50. Write an inequality to represent how many weeks (w) it will take her to save enough money. Combine like terms and solve for w.

• w <= 10

• w < 10

• w >= 10

• w > 10

5. A store is having a sale where each shirt costs $15 and each pair of pants costs $25. If a customer wants to spend no more than $120, write an inequality to represent the number of shirts (s) and pants (p) they can buy. Combine like terms and find the maximum number of shirts they can purchase if they buy 2 pairs of pants.

• 3 shirts

• 5 shirts

• 6 shirts

• 4

6. A farmer has 120 acres of land. He wants to plant corn and wheat, with corn taking 2 acres per field and wheat taking 3 acres per field. Write an inequality to represent the number of corn fields (c) and wheat fields (w) he can plant. Combine like terms and determine the maximum number of corn fields if he plants 10 wheat fields.

• 50

• 45

• 60

• 30

7. A student has a budget of $60 for books. If each textbook costs $12 and each novel costs $8, write an inequality to represent the number of textbooks (t) and novels (n) the student can buy. Combine like terms and find the maximum number of textbooks they can purchase if they buy 3 novels.

• 3

• 6

• 5

• 4

8. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the number of miles (m) they can drive. Combine like terms and solve for m.

• m ≤ 250

• m ≤ 150

• m ≤ 300

• m ≤ 200

9. A bakery sells cupcakes for $2 each and cookies for $1 each. If a customer wants to spend no more than $30, write an inequality to represent the number of cupcakes (c) and cookies (k) they can buy. Combine like terms and find the maximum number of cupcakes they can purchase if they buy 10 cookies.

• 20

• 10

• 15

• 5

10. A student is planning a party and has a budget of $150. If they plan to buy pizzas for $10 each and drinks for $2 each, write an inequality to represent the number of pizzas (p) and drinks (d) they can buy. Combine like terms and determine the maximum number of pizzas they can purchase if they buy 5 drinks.

• 12

• 16

• 14

• 10