# Inequality Word Problems

Inequality Word Problems
• Page 1
1.
The height of a person should not be less than 6 ft to get a police job. Choose an inequality for this situation.
 a. $x$ ≤ 6 b. $x$ < 6 c. $x$ > 6 d. $x$ ≥ 6

#### Solution:

The situation says that the height of a person should not be less than 6 ft.

Let the height of a person be x.

The inequality that represents the situation is x ≥ 6.
[Height of a person should be greater than or equal to 6 ft.]

2.
The price of a ball should not be more than $2. Choose an inequality for this situation.  a. $x$ ≤ 2 b. $x$ < 2 c. $x$ ≥ 2 d. $x$ > 2 #### Solution: The situation says that the price of a ball should not be more than$2.

Let the price of a ball be x.

The inequality that represents the situation is x ≤ 2.
[Price of a ball should be less than or equal to $2.] Correct answer : (1) 3. Ashley scores more than 400 marks on an average in all subjects. Choose an inequality to represent this situation.  a. $x$ < 400 b. $x$ ≥ 400 c. $x$ ≤ 400 d. $x$ > 400 #### Solution: The situation says that Ashley scores more than 400 marks. Let the average score be x. The inequality that represents the situation is x > 400. [Average score in all subjects should be greater than 400.] Correct answer : (4) 4. The sum of a number and 21 is less than or equal to 37. Find the number.  a. 14 b. 19 c. 18 d. 17 #### Solution: Let the number be n. n + 21 ≤ 37. [Write the inequality.] n ≤ 16 [Subtract 21 from both sides.] So, for the values of n ≤ 16 the inequality is satisfied. Correct answer : (1) 5. The sum of a number and 12 is greater than or equal to 57. Find the number.  a. 47 b. 43 c. 32 d. 20 #### Solution: Let the number be n. n + 12 ≥ 57. [Write the inequality.] n ≥ 45 [Subtract 12 from both sides.] So, for the values of n ≥ 45 the inequality is satisfied. Correct answer : (1) 6. Which of the graphs best suits for the inequality $x$ ≥ - 2?  a. Graph 2 b. Graph 1 c. Graph 3 d. Graph 4 #### Solution: The inequality x ≥ - 2 includes -2 as a solution. All the numbers to the right of the number on the line are greater than the number. [Values increase from left to right on a number line.] The graph with the open dot on a number shows that the number is not a solution of the inequality and the graph with the closed dot on a number shows that the number is a solution of the inequality. The following graph represents the solutions of the inequality. Correct answer : (4) 7. Gary has broken the university record of 17.05 seconds for a race. Which of the following cannot be Gary's timing in the race?  a. 11.85 b. 17.05 c. 16.05 d. 15.75 #### Solution: In order to break the record, Gary's timing in the race must be less than 17.05 seconds. [university record is 17.05 seconds.] The inequality, t < 17.05 best suits the timing of Gary. [Let t be the time taken by Gary to win the race.] All the choices except 17.05 are less than 17.05. [17.05 is equal to 17.05.] So, Gary's timing cannot be 17.05 seconds, if he breaks the university record. Correct answer : (2) 8. Which of the following inequalities best suits the graph?  a. $x$ < - 4.5 b. $x$ ≤ - 5 c. $x$ ≥ - 4.5 d. $x$ > - 5 #### Solution: All the numbers to the right of the number on the line are greater than the number. [Values increase from left to right on a number line.] An inequality is a statement that compares two expressions, of which one can be a variable. The graph with the open dot on a number shows that the number is not a solution of the inequality and the graph with the closed dot on a number shows that the number is a solution of the inequality. The graph has a closed dot on -5. So, -5 is not a solution of the inequality. Among the choices x > - 5 best suits the graph. Correct answer : (4) 9. Mrs. Katie has two sons admitted in different schools for kindergarten. The fee for the younger son is$32 and the fee for the elder son is more than the fee for the younger son. Which of the following is not a solution for the inequality expression $f$ that represents the total fee to be paid by Mrs. Katie?
 a. 114 b. 74 c. 94 d. 64

#### Solution:

The total fee to be paid by Mrs. Katie is greater than 32 + 32 = 64

The inequality for the total fee f, to be paid by Mrs. Katie is f > 64.

All the values that make the inequality true are the solutions of the inequality.

Among the choices all the values except 64 are greater than 64.

So, 64 is not a solution of the inequality.

10.
"The University $U$ offers hostel facilities for at most 800 students." Which of the following inequalities represent the situation, if $S$ is the number of students that the hostel can accommodate?
 a. $S$ ≥ 800 b. $S$ > 800 c. $S$ < 800 d. $S$ ≤ 800

#### Solution:

800 is also included in the solution because the hostel can accommodate at most 800 students.

The inequality for the situation is S ≤ 800.