WRITING AND SOLVING EQUATIONS FROM WORD PROBLEMS

Convert the following statements into equations and solve it.

Problem 1 :

5 added to a number is 9.

Solution :

Let x be the required number.

5+x = 9

Subtract 5 on both sides, we get

x = 9-5

x = 4

So, the required number is 4.

Problem 2 :

3 subtracted from a number is equal to 12.

Solution :

Let x be the required number.

x-3 = 12

Add 3 on both sides.

x = 12+3

x = 15

So, the required number is 15.

Problem 3 :

5 times a number decreased by 2 is 4.

Solution :

Let x be the required number.

5x-2 = 4

Add 2 on both sides.

5x = 4+2

5x = 6

Divide by 5 on both sides.

x = 4/5

Problem 4 :

2 times the sum of the number x and 7 is 13.

Solution :

Let x be the required number,

2x+7 = 13

Subtract 7 on both sides.

2x = 13-7

2x = 6

Divide by 2 on both sides.

x = 6/2

x = 3.

Problem 5 :

A number is 12 more than the other. Find the numbers if their sum is 48.

Solution :

Let x and y be two numbers.

x = 12+y

The sum of the numbers = 48

x+y = 48

12+y+y = 48

12+2y = 48

Subtract 12 on both sides.

2y = 48-12

2y = 36

Divide by 2 on both sides.

y = 36/2

y = 18

Problem 6 :

Twice the number decreased by 22 is 48. Find the number.

Solution :

Let x be the number

Twice a number = 2x

2x-22 = 48

Add 22 on both sides.

2x = 48+22

2x = 70

Dividing by 2.

x = 70/2

x = 35

Problem 7 :

Seven times the number is 36 less than 10 times the number. Find the number.

Solution :

7x-36 = 10x

7x-10x = 36

3x = 36

Dividing by 3, we get

x = 36/3

x = 12

Problem 8 :

The sum of two consecutive even number is 38. Find the numbers.

Solution :

Let x be the first even number. Its consecutive even number be x+2.

Sum of the even numbers = 38

x+(x+2) = 38

2x + 2 = 38

Subtract 2 on both sides, we get

2x = 38-2

2x = 36

Divide by 2 on both sides.

x = 36/2

x = 18

18 and 20 are required two consecutive even numbers.

Problem 8 :

The sum of three consecutive odd numbers is 51. Find the numbers.

Solution :

Let x be the first odd number.

x, x+2, x+4 are three consecutive odd numbers.

Sum of those three numbers = 51

x+(x+2)+(x+4) = 51

3x + 6 = 51

Subtract 6 on both sides.

3x = 51-6

3x = 48

Divide by 3 on both sides.

x = 48/3

x = 16

Problem 9 :

Rene is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages.

Solution :

Let x be Rene's younger sister's age.

Rene's age = x-6

After 10 years :

Rene's age = x-6+10 ==> x+4

Age of her younger sister = x+10

Rene's age + Her younger sister's age = 50

(x+4)+(x+10) = 50

2x+14 = 50

2x = 50-14

2x = 36

x = 18

Problem 10 :

A length of a rectangle is 10 cm more than its width. If the perimeter of the rectangle is 80 cm, find the dimensions of the rectangle.

Solution :

Let x be the width of the rectangle.

Length = x+10

Perimeter of the rectangle = 80

2(l+w) = 80

l+w = 40

x+10+x = 40

2x+10 = 40

2x = 30

x = 15