Question

Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find the integers.

Answer 1

Answer :

20 , 22 , 24

Solution :

• Note : Consecutive even integers differ by 2 .

Let three even consecutive integers be x , (x + 2) , (x + 4) .

According to the question , three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third .

Thus ,

=> x + 3(x + 2) = 2(x + 4) + 38

=> x + 3x + 6 = 2x + 8 + 38

=> x + 3x - 2x = 8 + 38 - 6

=> 2x = 40

=> x = 40/2

=> x = 20

Thus ,

1st integer = x = 20

2nd integer = x + 2 = 20 + 2 = 22

3rd integer = x + 4 = 20 + 4 = 24

Hence ,

The required integers are 20 , 22 , 24 .

Answer 2

Answer:

Let three consecutive even integers be x, x + 2, x + 4

According to statement

x + 3(x + 2) = 38 + 2(x + 4)

x + 3x + 6 = 38 + 2x + 8

4x + 6 = 2x + 46

4x - 2x = 46 - 6

2x = 40

x = 20

so integers are 20, 22, 24.