## SOLVING WORD PROBLEMS INVOLVING CONSECUTIVE INTEGERS

Solving Word Problems Involving Consecutive Integers :

In the section, we will learn how to solve word problems involving consecutive integers.

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers.

To solve word problems regarding consecutive integers, it is important to note :

Consecutive Integers :

If the first integer be x, then three consecutive integers be

x, x + 1, x + 2

Consecutive Even Integers :

If the first even integer be x, then three consecutive integers be

x, x + 2, x + 4

Consecutive Odd Integers :

If the first odd integer be x, then three consecutive integers be

x, x + 2, x + 4

Example 1 :

Find two consecutive natural numbers whose product is 30.

Solution :

Let x , (x + 1) be the two consecutive integers

Product of two consecutive integers  =  30

⋅ (x + 1)  =  30

x2 + 1x  =  30

x2 + x - 30  =  0

(x + 6) (x - 5)  =  0

 x + 6  =  0x  =  -6 x - 5  =  0 x  =  5

Since those are positive integer we should not take x  =  -6, let us take 5 as the value of x.

Therefore two consecutive integers are 5 and 6.

Verification :

Product of two positive integer is 30.

5 (6) = 30

30 =  30

Example 2 :

There are three consecutive positive integers such that the sum of the square of first and the product of the other two is 154. Find the integers.

Solution :

Let x, (x + 1) and (x + 2) be the first three consecutive integers

The sum of the squares of first and the product of the other two is 154

x2 + (x + 1) (x + 2)  =  154

x2 + x2 + 2x + 1x + 2  =  154

2x2 + 3x + 2  =  154

2x2 + 3x + 2 - 154  =  0

2x2 + 3x - 152  =  0

(2x + 19) (x - 8)  =  0

 2x + 19  =  02x  =  -19x  =  -19/2 x - 8  =  0x  =  8

Since it is positive integer, the value of x be 8.

Therefore three consecutive integers are 8, 9 and 10.

Verification :

The sum of the square of first and the product of the other two is 154.

82 + (9) (10)  =  154

64 + 90  =  154

154  =  154 After having gone through the stuff given above, we hope that the students would have understood how to solve word problems involving consecutive integers.

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