Okay so consecutive integers means that both the second number will come right after the first number. We can look at this as follows.

Number 1 = x

Number 2 = x+1

So if three times the first number is added to four times the second number, we can write this out as an equation, and solve for x.

3(Number 1)+4(Number 2)=88

Just substitute number 1 and number 2 with the equations we have written above.

3(x)+4(x+1)=88

Now all we have to do is solve for x. Simply add like terms and divide.

3x+4x+4=88

7x+4=88

7x=84

x=12

Therefore, plugging the number 12 in for x in our first equations, we can solve for both number 1 and number 2.

Number 1 = x = 12

Number 2 = x+1 = 12+1=13

So the smaller integer is 12