Question

Find three consecutive even integers such that the sum of the first and third increased by 18 is equal to three times the second.​

Answer 1

16, 18 and 20

Explanation:

x - an integer

2x - an even integer (the first)

Even integers increase by 1 so:

2x+2 - next consecutive integer (the second)

3(2x+2) - three times the second

2x+4 - the third consecutive integer

2x+2x+4 - the sum of the first and third

2x+2x+4+18 - the sum of the first and third increased by 18

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

4x + 22 = 6x + 6

-6 -6

4x + 16 = 6x

-4x -4x

16 = 2x

2x = 16

2x+2 = 18

2x+4 = 20

Check: 16+20+18=54; 3×18=54