# SOLVE LINEAR EQUATIONS WORD PROBLEMS

## About "Solve linear equations word problems"

Solve linear equations word problems :

"How to solve word problems of linear equations ?" is the question having had by almost all the students who study math in primary level.

There is a simple trick to understand "How to solve word problems of linear equations".

The picture given below tells us the trick.

## Solve linear equations word problems - Examples

Example 1 :

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Solution :

Let the breadth be x m.

The length will be (2x + 2) m.

Perimeter of swimming pool = 2(l + b) = 154 m

2(2x + 2 + x) = 154

2(3x + 2) = 154

Dividing both sides by 2,

3x + 2 = 77

Subtracting 2 on both sides, we get

3x + 2 - 2 = 77 - 2

3x = 75

On dividing 3 on both sides

x = 25

2x + 2 = 2 × 25 + 2 = 52

Hence, the breadth and length of the pool are 25 m and 52 m respectively.

Example 2 :

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Solution :

Let one number be x.

Therefore, the other number will be x+ 15.

According to the question,

x + x + 15 = 95

2x + 15 = 95

Subtract 15 on both sides

2x = 95 - 15

2x = 80

Divide by 2 on both sides

x = 40

x + 15 = 40 + 15 = 55

Hence, the numbers are 40 and 55.

Example 3 :

Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

Solution :

Let the common ratio between these numbers be x. Therefore, the numbers will be 5x and 3x respectively.

Difference between these numbers = 18

5x - 3x= 18

2x= 18

Divide by 2 on both sides

x = 9

First number = 5x= 5 × 9 = 45

Second number = 3x= 3 × 9 = 27

Hence the required numbers are 27, 45.

Example 4 :

Three consecutive integers add up to 51. What are these integers?

Solution :

Let three consecutive integers be x, x + 1, and x+ 2.

Sum of these numbers = x + x + 1 + x + 2 = 51

3x+ 3 = 51

Subtract by 3 on both sides

3x = 51 - 3

3x = 48

Divide by 3 on both sides

x = 16

x + 1 = 17

x + 2 = 18

Hence, the consecutive integers are 16, 17, and 18.

Example 5 :

The sum of three consecutive multiples of 8 is 888. Find the multiples.

Solution :

Let the three consecutive multiples of 8 be 8x, 8(x + 1), 8(x + 2).

Sum of these numbers = 8x + 8(x+ 1) + 8(x+ 2) = 888

8(x + x + 1 +x + 2) = 888

8 (3x + 3) = 888

Dividing by 8 both sides

3x+ 3 = 111

Subtract 3 on both sides

3x + 3 - 3 = 111 - 3

3x= 108

Divide by 3 on both sides

x = 36

First multiple = 8x = 8 × 36 = 288

Second multiple = 8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296

Third multiple = 8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304

Hence, the required numbers are 288, 296, and 304.

After having gone through the examples explained above, we hope that students would have understood "Solve linear equations word problems".

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear 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

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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

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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