Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

Let 3 consecutive integers: x, x+1, x+2
As per the question: 2x + 3(x+1) + 4(x+2) = 74
9x + 11 = 74
Transpose 11 to RHS
9x = 63
Divide both sides by 9
x = 63/9, x = 7
x = 7, x+1 = 7+1 = 8
x+2 = 7+2 = 9
Numbers are 7, 8 and 9