Solving and Graphing Inequalities in Real Life Scenarios

1. Sarah has 3 times as many apples as Tom. If Tom has x apples, write an inequality to show that Sarah has more than 10 apples. Solve for x and graph the solution on a number line.

• x = 5

• x < 2

• x > 3.33

• x ≤ 4

2. A concert hall has a seating capacity of 500. If each ticket costs $20, write an inequality to represent the number of tickets sold, x, such that the total revenue is less than $10,000. Solve for x and graph the solution.

• x < 500

• x < 400

• x ≤ 500

• x > 500

3. A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys x pencils and y erasers, write an inequality to show that the total cost is less than $10. Solve for y in terms of x and graph the solution.

• y < (30/3) - (1/3)x

• y < (50/3) - (4/3)x

• y < (20/3) - (5/3)x

• y < (40/3) - (2/3)x

4. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer has a budget of $50, write an inequality to represent the number of miles, m, they can drive. Solve for m and graph the solution.

• m ≥ 100

• m ≤ 100

• m = 50

• m < 100

5. A gardener has 20 feet of fencing to create a rectangular garden. If the length is represented by x and the width by y, write an inequality for the perimeter and solve for y in terms of x. Graph the solution on a number line.

• y = 10 - x

• y < 10 - x

• y ≤ 10 - x

• y ≥ 10 - x

6. A school is planning a field trip and has a budget of $1,200. If each student pays $15, write an inequality to represent the number of students, s, that can attend. Solve for s and graph the solution.

• s >= 100

• s < 80

• s <= 80

• s > 60

7. A recipe requires 2 cups of flour and 3 cups of sugar. If you have x cups of flour, write an inequality to show how many cups of sugar, y, you can use without exceeding 12 cups total. Solve for y in terms of x and graph the solution.

• y >= (12 - 2x) / 3

• y < (12 - 3x) / 2

• y <= (12 - 2x) / 3

• y = (12 - 2x) / 3 + 1

8. A factory produces x toys per hour. If the production goal is to make at least 200 toys in a day (8 hours), write an inequality and solve for x. Graph the solution on a number line.

• x < 25

• x > 50

• x = 30

• x >= 25

9. A book costs $15 and a magazine costs $5. If a person spends less than $50 on books and magazines, write an inequality to represent the number of books, b, and magazines, m, they can buy. Solve for m in terms of b and graph the solution.

• m < 5 - 2b

• m < 10 - 3b

• m < 8 - 2b

• m < 12 - 4b

10. A cyclist travels at a speed of x miles per hour. If they want to complete a 30-mile race in less than 2 hours, write an inequality for x and solve. Graph the solution on a number line.

• x = 15

• x > 15

• x < 30

• x < 15