Solving Linear Inequalities - Word Problems-Gr 7-Solved Examples

Solved Examples and Worksheet for Solving Linear Inequalities - Word Problems

Q1It cost 3 cents to copy a page. William has only $1.23 to spend on copying. Express the number of pages he can copy as an inequality.

A. x ≥ 41
B. x > 41
C. x ≤ 41
D. x < 41

Solutions

Step: 1

$1.23 = 123 cents.

[Converting dollars to cents]

Step: 2

Let x be the number of pages he can copy.

Step: 3

3x ≤ 123

[Original inequality.]

Step: 4

3x3 ≤ 1233

[Divide each side by 3.]

Step: 5

x ≤ 41

[Simplify.]

Correct Answer is : x ≤ 41

Q2Sam had to appear for four Math tests each having a total score of 30. The scores he got on three tests are 24, 24 and 27. How many points should he score on his fourth test, to have a total of at least 103 on all four tests?

A. at least 28
B. at most 27
C. at most 28
D. at least 33

Solutions

Step: 1

Let n be his score on the fourth test.

Step: 2

n + 24 + 24 + 27 ≥ 103

[Original inequality.]

Step: 3

n + 75 ≥ 103

[Simplify.]

Step: 4

n + 75 - 75 ≥ 103 - 75

[Subtract 75 from each side.]

Step: 5

n ≥ 28

[Simplify.]

Step: 6

Sam should get at least 28 in the fourth test.

Correct Answer is : at least 28

Q3Every night Sheela spends at least 4 hours studying. Which of the following numbers is a solution for the inequality expression h, the number of hours she spends studying?
A. 3
B. 2
C. 4
D. None of the above

Solutions

Step: 1

From the problem, the number of hours Sheela spends studying is more than or equal to 4.

[Atleast 4 implies that the number is more than or equal to 4.]

Step: 2

So, the inequality for the number of hours she spends studying is h ≥ 4.

[h is the number of hours Sheela spends studying.]

Step: 3

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

Step: 4

Among the choices, 4 is a solution of the inequality.

[The number of hours can be equal to 4, but not less than 4.]

Correct Answer is : 4

Q4Gary has 4 pairs of shoes and his brother Tommy has more than 9 pairs of shoes. Which of the following numbers is not a solution for the inequality expression s, the total number of pairs of shoes possessed by Gary and Tommy?
A. 16
B. 15
C. 12
D. 18

Solutions

Step: 1

The total number of pairs of shoes possessed by Gary and Tommy is more than 13.

Step: 2

The inequality for the total number of pairs of shoes possessed by Gary and Tommy is s > 13.

Step: 3

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

Step: 4

Among the choices, 12 is not a solution of the inequality.

Correct Answer is : 12

Q5George went shopping and spent $274. By the time he came back to his house, he had at least $84 in his pocket. How much did he have before he went shopping?

A. At least $358
B. $358
C. At most $442
D. None

Solutions

Step: 1

Let m be the amount George had in his pocket before he went shopping.

Step: 2

Money in George's pocket before shopping - Money spent ≥ Money left over

Step: 3

m - 274 ≥ 84

[Original inequality.]

Step: 4

m - 274 + 274 ≥ 84 + 274

[Add 274 to each side.]

Step: 5

m ≥ 358

[Simplify.]

Step: 6

George had at least $358 before he went shopping.

Correct Answer is : At least $358

Q6Katie has $186, with which she can buy at most 3 dresses. Find the maximum cost of each dress she can buy.

A. $63
B. $62
C. $61
D. None of the above

Solutions

Step: 1

Let x be the cost of each dress.

Step: 2

As she can buy at most 3 dresses, the total cost of the 3 dresses is less than or equal to $186.

Step: 3

3x ≤ 186

[Write the inequality.]

Step: 4

3x3 ≤ 1863

[Divide by 3 on each side.]

Step: 5

x ≤ 62

[Simplify.]

Step: 6

The maximum cost of each dress is $62.

[As x ≤ 62, the maximum value of x is 62.]

Correct Answer is : $62

Q7How old is Nathan now, if he will be above 15 after 6 years?
A. 9 years
B. Above 9 years
C. Below 9 years
D. None of the above

Solutions

Step: 1

Let a be the present age of Nathan.

Step: 2

a + 6 > 15

[Write an inequality.]

Step: 3

a + 6 - 6 > 15 - 6

[Subtract 6 from each side.]

Step: 4

a > 9

[Simplify.]

Step: 5

Nathan's present age is above 9 years.

Correct Answer is : Above 9 years

Q8The sum of two numbers is more than 292. If one of the numbers is 181, then which of the following numbers can be the other number?

A. 110
B. 117
C. 108
D. 109

Solutions

Step: 1

The sum of two numbers is more than 292.

[In words.]

Step: 2

Let x be the unknown number.

Step: 3

x + 181 > 292

[Original Inequality.]

Step: 4

x + 181 - 181 > 292 - 181

[Subtract 181 from each side.]

Step: 5

x > 111

[Simplify.]

Step: 6

The other number is greater than 111.

Step: 7

Among the choices, the number greater than 111 is 117.

Step: 8

So, 117 is the other number.

Correct Answer is : 117

Q9Rose wants to buy 9 burgers for her friends. She cannot spend more than $90. Find the maximum cost of each burger if she buys 9 burgers.
A. $11.32
B. $11
C. $9
D. $10

Solutions

Step: 1

Let x be the cost of each burger.

Step: 2

9x ≤ 90

[Original inequality.]

Step: 3

9x9 ≤ 909

[Divide by 9 on each side.]

Step: 4

x ≤ 10

[Simplify.]

Step: 5

The maximum cost of each burger is $10.

Correct Answer is : $10

Q10To qualify in an examination, a candidate has to get a total of 150 in two tests. Victor appeared for the exam and scored 80 in the first test. If he was qualified for the exam, then how much did he score in the second test?
A. 50
B. 60
C. 65
D. 70

Solutions

Step: 1

The total score in the two tests should at least be 150.

Step: 2

Let m be the score obtained by Victor in the second test.

Step: 3

80 + m ≥ 150

[Original inequality.]

Step: 4

80 + m - 80 ≥ 150 - 80

[Subtract 80 from each side.]

Step: 5

m ≥ 70

[Simplify.]

Step: 6

Among the choices, the value which satisfies the inequality is 70.

Step: 7

So, Victor scored 70 in the second test.

Correct Answer is : 70

Q11Edward wants to withdraw $1382.75 from his savings bank account. The minimum balance to be in any savings account is $500. What is the amount that should be there in Edward's account?
A. $1858.51
B. $1882.75
C. $1870.50
D. $1828.51

Solutions

Step: 1

Let a be the amount in Edward's savings account.

Step: 2

a - 1382.75 ≥ 500

[Write an inequality.]

Step: 3

a - 1382.75 + 1382.75 ≥ 500 + 1382.75

[Add 1382.75 to each side.]

Step: 4

a ≥ 1882.75

[Simplify.]

Step: 5

Edward should have atleast $1882.75 in his account.

Correct Answer is : $1882.75

Q12Thirty six less than a number is greater than fifty seven. Which of the choices can be the number?

A. 89
B. 91
C. 92
D. 95

Solutions

Step: 1

Let x be the number.

Step: 2

x - 36 > 57

[Original inequality.]

Step: 3

x - 36 + 36 > 57 + 36

[Add 36 to each side.]

Step: 4

x > 93

[Simplify.]

Step: 5

Among the choices, the number greater than 93 is 95.

Correct Answer is : 95

Q13Write an inequality for the set of integers that, when divided by -6, gives a result not more than 10.
A. n < -60
B. n ≥ - 60
C. n ≤ -60
D. None of the above

Solutions

Step: 1

Let n be an integer which does not give more than 10 when it is divided by -6.

Step: 2

As the quotient of the division is not more than 10, the result can be any number less than or equal to 10.

Step: 3

n-6 ≤ 10

[Wite the inequality.]

Step: 4

-6n-6 ≥ 10 × (-6)

[Multiply by - 6 on each side and reverse the inequality symbol.]

Step: 5

n ≥ - 60

[Simplify.]

Correct Answer is : n ≥ - 60

Q14The sum of a number and 13 is less than or equal to 7. Find the number.
A. - 6
B. 6
C. 5
D. - 5

Solutions

Step: 1

Let n be the number

Step: 2

Sum of number and 13 = n + 13

Step: 3

n + 13 ≤ 7

Step: 4

n + 13 - 13 ≤ 7 - 13

[Subtract by 13 on both the side]

Step: 5

n ≤ - 6

Correct Answer is : - 6

Q15Product of a number and 6 is greater than or equal to 102. Find the number.

A. 15
B. 16
C. 17
D. 14

Solutions

Step: 1

Let the number be n.

Step: 2

n × 6 ≥ 102

[Write the inequality.]

Step: 3

⇒ n ≥ 17

[Divide by 6 on both sides.]

Step: 4

So, for the values of n ≥ 17 the inequality is satisfied.

Correct Answer is : 17

Solved Examples and Worksheet for Solving Linear Inequalities - Word Problems

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