WORD PROBLEMS ON LINEAR EQUATIONS IN ONE VARIABLE 

Problem 1 :

When three times a certain number is subtracted from 15, the result is -6. Find the number.

Solution:

Let the number be x.

15 - 3x = -6

3x = 15 + 6

3x = 21

x = 7

So, the number is 7.

Problem 2 :

Five times a certain number, minus 5, is equal to 7 more than three times the number. What is the number?

Solution:

Let the number be x.

5x - 5 = 7 + 3x

5x - 3x = 7 + 5

2x = 12

x = 6

So, the number is 6.

Problem 3 :

Three times the result of subtracting a certain number from 7 gives the same answer as adding eleven to the number. Find the number.

Solution:

Let x be the number.

3(7 - x) = x + 11

21 - 3x = x + 11

4x = 10

x = 10/4

x = 5/2

Problem 4 :

I think of a number. If I divide the sum of 6 and the number by 3, the result is 4 more than one quarter of the number. Find the number.

Solution:

So, the number is 24.

Problem 5 :

The sum of two numbers is 15. When one of these numbers is added to three times the other, the result is 27. What are the numbers?

Solution:

Let two numbers are x and y.

x + y = 15

x = 15 - y ---> (1)

x + 3y = 27 ---> (2)

Substitute x = 15 - y in (2)

(15 - y) + 3y = 27

15 + 2y = 27

2y = 27 - 15

2y = 12

y = 6

By applying y = 6 in (1)

x + 6 = 15

x = 15 - 6

x = 9

Problem 6 :

What number must be added to both the numerator and the denominator of the fraction 2/5 to get the fraction 7/8?

Solution:

Let the number be x.

Problem 7 :

What number must be subtracted from both the numerator and the denominator of the fraction 3/4 to get the fraction 1/3?

Solution:

Let the number be x.

Problem 8 :

Eli is now one-quarter of his father's age and in 5 years time his age will be one-third the age of his father. How old is Eli now?

Solution:

In 5 years,

Eli is 10 years now, and his father is 40 years.

Problem 9 :

When Maria was born her mother was 24 years old. At present Maria's age is 20% of her mother's age. How old is Maria now?

Solution:

Let the ages of Maria and her mother be x and x + 24 respectively.

x = 0.2(x + 24)

x = 0.2x+4.8

x - 0.2x + 4.8

0.8x = 4.8

x = 4.8/0.8

x = 6

Therefore, the present age of Maria is 6 years.

Problem 10 :

Five years ago Jacob was one-sixth the age of his brother. In three years time his age doubled will match his brother's age. How old is Jacob now?

Solution:

Let J = Jacob's current age

Let B = brother's current age

3 years from now

Jacob's age is J + 3

brother's age is B + 3

2(J + 3) = B + 3

2J + 6 = B + 3

2J - B = -3 ---> (2)

Subtract equation (2) from (1)

4J = 28

J = 28/4

J = 7

So, Jacob is 7 years old.