Worksheet on Word Problems on Linear Equation will be of much help in practicing problems on the linear equations. If you would like to know more about the linear equation concept then the Linear Equations Word Problems Worksheet with Answers can be of utmost help. Linear Equation Word Problems Worksheet PDF can be a great resource to practice a variety of word problems. Step by Step Solutions provided for all the problems makes it easy for you to understand the concept in a fun and engaging manner.

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## Linear Equations Word Problems Worksheet with Answers PDF

**I. **Two third of a number is 52. Find 50% of the number?

**Solution:**

Given that,

Two third of the number is 52.

Let the number be x.

2/3(x)=52

x=52 × 3/2

=78

50% of the number=1/2(78)

=39

Therefore, 50% of the number is 39.

**II. **The difference between the two numbers is 12. The ratio of the two numbers is 5 : 3. What are the two numbers?

**Solution:**

Given that,

The difference between the two numbers is =12

The ratio of the two numbers is =5 : 3

Let the two numbers be x,y.

x-y=12 –>(1)

x/y=5/3 —>(2)

x=5/3y

substitute x in (1)

5/3y-y=12

2y/3=12

2y=36

y=18

Substitute y in Eqn(1)

x-y=12

x-18=12

x=18+12=30

Therefore, Two numbers are 30, 18.

**III. **Sum of the two numbers is 70. If one exceeds the other by 10, Find the numbers?

**Solution:**

Given that,

Sum of the two numbers is= 70

Let x be one of the two numbers.

Then, the other number is (x + 10).

So, we have

x + (x + 10) = 70

x + x + 10 = 70

2x + 10 = 70

Subtract 10 from each side.

2x + 10 – 10 = 70 – 10

2x = 60

Divider each side by 2.

2x/2 = 60/2

x = 30

x + 10 = 30 + 10

x + 10 = 40

Hence, the two numbers are 30 and 40.

**IV. **The perimeter of a rectangular swimming pool is 120 m. Its length is 4 m more than thrice its width. What are the length and the width of the pool?

**Solution:**

Given that,

The perimeter of a rectangular swimming pool is =120 m

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

Also given Length is 4 m more than thrice its width.

So, the length is l = 4w + 4

The perimeter of the swimming pool is 120 m.

2l + 2w = 120

Plug l = 4w + 4

2(3w + 4) + 2w = 120

6w+8+2w=120

8W+8=120

Subtract 8 from each side

8w+8-8=120-8

8w=112

w=112/8=14 m

Therefore, length=4w+4

=4(14)+4

=56+4

=60 m

Therefore, the length and width of the pool are 14 m and 60 m.

**V. **Vijaya is 5 years older than her younger sister. After 10 years, the sum of their ages will be 45 years. Find their present ages?

**Solution:**

let the age of younger sister be X and Vijaya=x+5

after10 years younger sister age=x+10and Vijaya=x+10+5

x+10+x+15=45

2x+25=45

x=45-25/2

=20/2

=10

The age of Vijaya=x+5 years=10+5=15 years.

The age of younger sister=10years.

Therefore, the age of Vijaya is 15 years, and her younger sister is 10 years.

**VI. **In a class of 64 students, the number of boys is 3/5 of the number of girls. Find the number of boys and girls in the class?

**Solution:**

Let the number of girls be x.

So, 3/5x + x = 64

3x+5x/5=64

8x = 320

x=320/8=40

The number of girls is 40

So the number of boys is 3/5(40)=24

Therefore, the number of boys and girls in the class are 24 and 40.

**VII. **Among two supplementary angles, the measure of the larger angle is 42 more than the measure of the smaller. Find their measures?

**Solution:**

Given that,

The measure of the larger angle is 42 more than the measure of the smaller.

Let us assume supplementary be x^{0} and (180−x)^{0}.

Let the larger angle be x^{0}.

Then,

(180−x)+42=x

222-x=x

222=2x

x=222/2=111

Larger angle=111^{0}.

Smaller angle=(108-42)=66^{0}.

Therefore, the Larger angle is 111^{0} and the smaller angle is 66^{0}.

**VIII. **In an isosceles triangle, the base angles are equal and the vertex angle is 60°. Find the measure of the base angles?

**Solution:**

Let the base angle be x.

Another base angle =x.

Angle sum property of triangle

2x+60=180^{0}

2x=180-60

2x=120

x=120/2=60^{0}

First base angle=60^{0}=second base angle.

Therefore, the measure of base angles is 60^{0}.

**Ix. **The sum of two consecutive even numbers is 30. Find the numbers?

**Solution:**

Given that,

The sum of two consecutive even numbers is =30

Let’s assume the two consecutive even numbers are x and x+2.

According to the question,

The Sum of x and x+2 =30.

We have,

x+(x+2)=30

2x+2=30

2x=30-2

2x=28

x=28/2=14

x+2=14+2=16

Therefore, the two consecutive numbers are 14 and 16.

**X. **The denominator of a fraction is greater than the numerator by 6. If the numerator is increased by 3 and the denominator is decreased by 1, the number obtained is 4/5, find the fraction?

**Solution:**

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 6.

The rational number will be x/x+6

According to the given condition,

x+3/x+6-1=4/5

x+3/x+5=4/5

5(X+3)=4(x+5)

5x+15=4x+20

5x+15-4x-20=0

x-5=0

x=5

The rational number will be x/x+6

=5/5+6

=5/11

Therefore, the rational number is 5/11.

**XI. **Laxman’s father is 66 years old. he is 6 years older than six times adman’s age. what is adman’s age?

**Solution:**

Let Adam’s father’s present age be f.

Let Adam’s present age be a.

f=66

f=6+6a

66=6+6a

60=6a

a=60/6=10

Hence, Adam’s age is 10years.

**XII. **Convert the following statements into equations.

(a) 4 added to a number is 10.

(b) 2 subtracted from a number is equal to 14.

(c) 5 times a number decreased by 2 is 13.

(d) 4 times the sum of the numbers x and 5 is 40.

**Solution:**

(a) Let the number be x.

4+x=10

(b) Let the number be x.

x-2=14

(c) Let the number be x.

5x-2=13

(d) 4(x+5)=40