**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,

**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 ?

**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

Add 1/2 to each side.

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 4 2/15 cm.

x + x + 4/3 = 4 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 = 1⅖

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.

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