WORD PROBLMES ON CONSECUTIVE NUMBERS

Problem 1 :

The sum of three consecutive integer is 39. Find the middle number.

Solution :

Let x be the first number.

Its consecutive number will be x + 1 and x + 2.

Sum of three consecutive integers = 39

x + x + 1 + x + 2 = 39

3x + 3 = 39

3x = 36

x = 36/3

x = 12

x + 1 = 13

x + 2 = 14

So, the consecutive three numbers are 12, 13 and 14.

Problem 2 :

Twice the smallest of three consecutive odd integer is seven more than the largest. Find the three integers.

Solution :

Three consecutive odd integers are x, x + 2 and x + 4.

Smallest number = x 

Largest number = x + 4

2x = 7 + (x + 4)

2x = 7 + x + 4

2x - x = 11

x = 11

x + 2 = 13

x + 4 = 15

So, the three consecutive numbers are 11, 13 and 15.

Problem 3 :

Five times the second of three consecutive even integer is eighteen less than three times the sum of the first and third integers. Find the consecutive even integer.

Solution :

Three consecutive even integers are x, x + 2 and x + 4.

5(x + 2) = 3(x + x + 4) - 18

5x + 10 = 3(2x + 4) - 18

5x + 10 = 6x + 6 - 18

5x - 6x = -12 - 10

-x = -22

x = 22

x + 2 = 24

x + 4 = 26

So, the three even numbers are 22, 24 and 26.+

Problem 4 :

Find three consecutive odd integers such that three times the second number added to twice the third number is seven times the first number.

Solution :

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

3(x + 2) + 2(x + 4) = 7x

3x + 6 + 2x + 8 = 7x

5x + 14 = 7x

5x - 7x = -14

-2x = -14

x = 14/2

x = 7

The three consecutive odd numbers are 7, 9 and 11.

Problem 5 :

Find the measure of a angle is supplement measures 4 less than three times its complement.

Solution :

Let x be the angle.

Its supplementary = 180 - x 

Its complementary = 90 - x

180 - x = 3(90 - x) - 4

180 - x = 270 - 3x -4

180 - x = -3x + 266

-x + 3x = 266 - 180

2x = 86

x = 43

The required angle is 43.

Problem 6 :

Find three consecutive number such that the sum of the largest and 5 times the smallest is -244.

Solution :

Three consecutive numbers are x, x + 1 and x + 2.

x + 2 + 5x = -244

6x + 2 = -244

6x = -244 - 2

-6x = -246

x = 246/6

x = 41

x + 1 = 42

x + 2 = 43

So, three consecutive numbers are 41, 42 and 43.

Problem 7 :

Find three consecutive even integers such that the sum of twice the smallest and 4 times the largest is 304.

Solution :

Three consecutive even numbers are x, x + 2 and x + 4.

2x + 4(x + 4) = 304

2x + 4x + 16 = 304

6x + 16 = 304

6x = 304 - 16

6x = 288

x = 288/6

x = 48

So, the required numbers are 48, 50 and 52.