Answer:
The smallest possible value of a+b+c+d is: 4
Step-by-step explanation:
since we are given that:
4a - 13 = 6b + 35 = 8c -17 = d
<em>on taking the first two equality i.e. 4a-13=6b+35</em>
we get 
<em>on using the first and third equality we have:</em>
4a-13=8c-17

<em>also from the first and last equality we have:</em>
d=4a-13
Hence,


the smallest possible value such that the expression a+b+c+d is positive will be claculated as:
a+b+c+d>0
that means 

But as a is an integer, hence the smallest such value is 4.