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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.]


Correct answer : (4)
 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.


Correct answer : (4)
 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.


Correct answer : (4)

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