Question

Find three consecutive even integers such that the sum of the first and third is 6 less than three times the second.

Answer 1

4, 6, 8

Explanation:

For many "consecutive integer" problems, it is convenient to let a variable represent their average. Here, we can let x represent the middle integer.

The sum of the first and third is (x -2) +(x +2) = 2x.

Three times the second, less 6 is 3x -6.

These expressions are equal:

3x -6 = 2x

x = 6 . . . . . . . . . . add 6-2x to both sides

The middle integer is 6, so ...

the consecutive even integers are 4, 6, 8.

______

Check

The sum of the first and third is 4+8 = 12. 6 less than 3 times the second is 3(6)-6 = 12. The answer checks.