Grade 12 Inequality Word Problems Worksheet

Inequality Word Problems

Read each word problem carefully, set up the appropriate inequality, solve it, and interpret your solution in the context of the problem. Show all your work.

1. A store sells laptops for $800 each. They want to make a profit of at least $12,000 this month. If their fixed costs are $4,000, and they have already sold 5 laptops, how many more laptops must they sell to reach their profit goal?

2. The height 'h' (in meters) of a projectile launched vertically upwards is given by the equation h(t) = -5t² + 40t + 10, where 't' is the time in seconds. During what time interval is the projectile at a height of at least 70 meters?

3. A machine produces cylindrical rods. The ideal diameter of a rod is 20 mm. The machine is considered to be working correctly if the absolute difference between the actual diameter (d) and the ideal diameter is no more than 0.5 mm. Write an absolute value inequality that represents the acceptable range of diameters for the rods, and solve it.

4. A company's revenue R (in thousands of dollars) from selling 'x' units of a product is given by R(x) = 15x. The cost C (in thousands of dollars) is given by C(x) = 5x + 30. For the company to make a profit, the revenue must be greater than the cost. The inequality representing this condition is  . The solution to this inequality is  . This means the company must sell more than   units to make a profit.

5. A student needs to score an average of at least 80% on five tests to pass a course. Their scores on the first four tests are 75%, 82%, 78%, and 85%. What is the minimum score the student needs on the fifth test to pass the course?

6. A rectangular garden has a length that is 5 meters more than its width. If the perimeter of the garden is at most 70 meters, and the area of the garden must be at least 200 square meters, determine the possible range of values for the width of the garden.