67.2k views
1 vote
Find three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.

1 Answer

0 votes

Answer:

2, 4, 6

Explanation:

You want three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.

Setup

Let x represent the middle integer. Then the first is (x-2) and the third is (x+2). The given relation is ...

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

Solution

Simplifying the equation gives ...

2x -4 +3x = 2x +4 +4

5x -4 = 2x +8 . . . . . . . collect terms

3x = 12 . . . . . . . . . . . add 4-2x

x = 4 . . . . . . the middle integer

The integers are 2, 4, 6.

__

Additional comment

It often simplifies the equation if the variable is used to represent the middle of the consecutive integers in problems like this. In this particular problem, there is not a great advantage.

<95141404393>

User Herka
by
8.0k points