# LINEAR INEQUALITIES WORD PROBLEMS

## About "Linear inequalities word problems"

Linear inequalities word problems play a major role quantitative aptitude test. There is no competitive exam without the questions from this topic. Even though we have been already taught this topic in our school days, we need to learn some more short cuts which are being used to solve the word problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams

## Why do students have to study this topic?

Students who are preparing to improve their aptitude skills and those who are preparing for competitive exams must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic "Linear inequalities word problems" Whether a person is going to write placement exam to get placed or a student is going to write a competitive exam in order to get admission in university, he must be prepared to solve linear inequalities word problems.This is the reason for why people must study this topic.

## Benefit of studying this topic

As we mentioned in the above paragraph, a person who wants to get placed in a company must write placement test and a student who wants to get admission in university for higher studies must write entrance exam. To meet the above requirements, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned.

## How can students do linear inequalities word problems?

Students have to learn few basic operations in this topic  and some additional tricks. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to do the word problems which are being asked from this topic in competitive exams. The stuff which I have mentioned above are nothing but "less than, less than or equal to,  greater than & greater than or equal to"

## Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve word problems related to linear inequalities. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some word problems on linear inequalities. You can check your answer online and see step by step solution.

1. An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. "x" and "y" can be related by the inequality

(A)   x + y ≠ 9

(B)   x + y ≤ 9

(C)   x + y ≥ 9

(D)   None of these
jQuery UI Accordion - Default functionality
Let "x" and "y" be the number of experienced person and fresh workmen respectively.

Total number of people recruited = x + y

As per the question, total number of people (experienced + fresh) recruited should not be more than 9.

That is, total number of people (x+y) recruited should be equal to 9 or less than 9.

So, we have x + y≤ 9

Hence, option "B" is correct

2. On the average experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. This situation can be expressed as

(A)   5x + 3y ≤ 30

(B)   5x + 3y > 30

(C)   5x + 3y ≥ 30

(D)   None of these
jQuery UI Accordion - Default functionality
Let "x" and "y" be the number of experienced person and fresh workmen respectively.

Total number of units of work done by experienced person per day = 5x

Total number of units of work done by fresh one per day = 3y

Total number of units of work done by both experienced person and fresh one per day = 5x + 3y

As per the question, total number of units of work per day should be at least 30 units.

That is, total number of units of work (5x+3y) should be equal to 30 or more than 30.

So, we have 5x + 3y ≥ 30

Hence, option "C" is correct

3. The rules and regulations demand that the employer should employ not more than 5 experienced hands (x) to 1 fresh one (y) and this fact can be expressed as

(A)   5y > x

(B)   5y ≤ x

(C)   5y ≥ x

(D)   None of these
jQuery UI Accordion - Default functionality
Let "x" and "y" be the number of experienced hands and fresh hands respectively.

As per the question, no. of experienced hands(x) should not be more than 5

That is, no. of experienced hands should be equal to 5 or less than 5

So, we have x ≤ 5 or x/5 ≤ 1 ------(1)

As per the question, no. of fresh hands is equal to 1

So, we have y = 1

In (1), replacing 1 by "y", we get x/5 ≤ y ------(2)

In (2), by multiplying 5, we get x ≤ 5y (or) 5y ≥ x

Hence, option "C" is correct

4. The union however forbids the employer to employ less than 2 experienced persons (x) to each fresh person (y). This situation can be expressed as

(A)   x ≤ y/2

(B)   y ≤ x/2

(C)   y ≥ x/2

(D)   None of these
jQuery UI Accordion - Default functionality
Let "x" & "y" be the no. of experienced and fresh hands respectively.

In this problem, the word "forbid" plays an important role.
Meaning of "Forbid" is "Not allowed"

The union forbids the employer to employ less than 2 experienced hands
That is, the union does not allow the employer to employ less than 2 experienced hands

Therefore, the employer should employ 2 or more than 2 experienced hands.

So, we have x ≥ 2 or x/2 ≥ 1 ------(1)

And also, no. of fresh persons to be employed is equal to 1

So, we have y = 1

In (1), replacing 1 by "y", we get x/2 ≥ y or y ≤ x/2

Hence, option "C" is correct

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