LINEAR INEQUALITIES WORD PROBLEMS

We can follow the steps given below to solve linear inequalities word problems.

Step 1 :

Read and understand the information carefully and translate the statements into linear inequalities. 

Step 2 :

Solve for the variable using basic operations like addition, subtraction, multiplication and division.

Step 3 :

Find the solution set and obtain some of the possible solutions.

Apart from the above steps, we have to make the following changes, when we multiply or divide each side of the inequality by a negative value. 

•  If we have  <, then change it as  >
•  If we have  >, then change it as  <
•  If we have  ≤, then change it as  ≥
•  If we have  ≥, then change it as  ≤

Problems

Problem 1 :

In 2010 Sacramento, California, received 23 inches in annual precipitation. In 2011, the city received 17 inches in annual precipitation. In which year was there more precipitation ?

Solution : 

Locate the two integers 23 and 17 on a number line and mark them.

23 is to the right of 17 on the number line.

This means that 23 is greater than 17.

We can write the above situation in terms of inequality as

23 > 17

17 is to the left of 23 on the number line.

This means that 17 is less than 23.

We can write the above situation in terms of inequality as

17 < 23

So, there was more precipitation in 2010.

Problem 2 : 

An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. Find the inequality which can relate x and y. 

Solution :

Given : x and y stand for number of experienced person and fresh workmen respectively. 

Total number of people recruited  is

=  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. 

That is

x + y  ≤  9

Problem 3 : 

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 

Solution :

Given : x and y stand for number of experienced person and fresh workmen respectively. 

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

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

Total number of units of work done by both experienced person and fresh one per day is 

=  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, this situation can be expressed as

5x + 3y  ≥  30

Problem 4 :

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

Solution :

Given : x and y stand for number of experienced person and fresh workmen 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)

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

So, we have

y  =  1

Substitute y for z in (1). 

(1)-----> x/5  ≤  y

Multiply each side by 5.

x  ≤  5y    (or)    5y  ≥  x

So, the situation can be expressed as 

x  ≤  5y    (or)    5y  ≥  x

Problem 5 :

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

Solution :

Given : x and y stand for number of experienced person and fresh workmen 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. 

Then, we have

x  ≥  2    (or)    x/2  ≥  1 -----(1)

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

Then, we have

y  =  1

Substitute y for 1 in (1).

(1)-----> x / 2  ≥  y     (or)    y  ≤  x / 2

So, the situation can be expressed as 

x / 2  ≥  y     (or)    y  ≤  x / 2

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6