# WORKSHEET ON WORD PROBLEMS ON LINEAR EQUATION IN ONE VARIABLE

Worksheet on Word Problems on Linear Equations in One Variable :

Worksheet given in this section is much useful to the students who would like to practice solving word problems on linear equations in one variable.

Before look at the worksheet, if you would like to know the stuff related to solving linear equations in one variable,

## Worksheet on Word Problems on Linear Equation in One Variable - Problems

Problem 1 :

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

Problem 2 :

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

Problem 3 :

If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number.

Problem 4 :

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

Problem 5 :

The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15 cm. What is the length of either of the remaining equal sides ? ## Worksheet on Word Problems on Linear Equation in One Variable - Solutions

Problem 1 :

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

Solution :

Let x be one of the two numbers.

Then, the other number is (x + 15).

Given : Sum of two numbers is 95.

So, we have

x + (x + 15)  =  95

Simplify.

x + x + 15  =  95

2x + 15  =  95

Subtract 15 from each side.

2x + 15 - 15  =  95 - 15

2x  =  80

Divider each side by 2.

2x/2  =  80/2

x  =  40

x + 15  =  40 + 15

x + 15  =  55

Hence, the two numbers are 40 and 55.

Problem 2 :

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

Solution :

From the ratio 5 : 3, the two numbers can be assumed as

5x and 3x

Given : The two numbers differ by 18.

So, we have

5x - 3x  =  18

2x  =  18

Divide each side by 2.

2x/2  =  18/2

x  =  9

5x  =  5(9)  =  45

3x  =  3(9)  =  27

Hence, the two numbers are 45 and 27.

Problem 3 :

If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number.

Solution :

Let x be the required number.

From, the given information, we have

(x - 1/2) ⋅ 1/2  =  1/8

Multiply each side by 2.

(x - 1/2) ⋅ 1/2 ⋅ 2  =  1/8 ⋅ 2

x - 1/2  =  1/4

x - 1/2 + 1/2  =  1/4 + 1/2

x  =  1/4 + 2/4

x  =  (1 + 2)/4

x  =  3/4

Hence, the required number is 3/4.

Problem 4 :

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

Solution :

Let l be the length and w be the width of the swimming pool.

Given : Length is 2 m more than twice its width.

So, the length is

l  =  2w + 2

Given : The perimeter of the swimming pool is 154 m.

2l + 2w  =  154

Plug l  =  2w + 2

2(2w + 2) + 2w  =  154

Simplify.

4w + 4 + 2w  =  154

6w + 4  =  154

Subtract 4 from each side.

6w + 4 - 4  =  154 - 4

6w  =  150

Divide each side by 6.

6w / 6  =  150 / 6

w  =  25

Then, the length is

l  =  2(25) + 2

l  =  50 + 2

l  =  52

Hence, the length and width of the rectangular swimming pool are 52 m and 25 m respectively.

Problem 5 :

The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15 cm. What is the length of either of the remaining equal sides ?

Solution :

Let x be the length of each of the remaining two equal sides.

So, the sides of the triangle are

x, x and 4/3 Given : The perimeter of the triangle is 2/15 cm.

x + x + 4/3  =  2/15

2x + 4/3  =  62/15

Subtract 4/3 from each side.

2x + 4/3 - 4/3  =  62/15 - 4/3

2x  =  62/15 - 20/15

2x  =  (62 - 20)/15

2x  =  42/15

2x  =  14/5

Divide each side by 2.

2x ÷ 2  =  (14/5) ÷ 2

x  =  7/5

x  =  1

Hence, the length of either of the remaining equal sides is 1⅖ cm. After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems using linear equations with one variable.

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

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

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

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 