Two consecutive even integers such that their son is equal to the difference of three times the larger and two times smaller

Answer 1

We need a bit of algebra for this one...

x, y (two integers, x is smaller)

x, x+2 (consecutive even integers, so we know y in terms of x)

(x + y) (sum x, y)

(3y - 2x) (difference of three times the larger, and two times the smaller)

hence we have an equation

x + y = 3y - 2x

=> 3x = 2y

substitute (x + 2) to get 3x = 2(x + 2)

=> 3x = 2x + 4

=> x = 4

We know next number is x + 2 so y = 6

Double-check our workings: two consecutive even numbers? yes! sum of the two is 10. three times the larger is 18. 2 times smaller is 8. difference = 10. All good!