The smiths counted 11 riders and 26 wheels passing by. there were no unicycles, only bicycles and tricycles with only one rider. how many more bicycles than tricycles did they see?

I only one person rode a tricycle - that would leave 23 wheels and you cannot make a complete number of bicycles
If 2 people rode tricycles that would leave 20 wheels which would seat 10 bicyclists.
But that totals up to 12 people

3 people riding tricyles leaves 15 wheels which will not complete a number of bicycles

4 people riding tricycles (4 x 3) leaves 14 wheels for 7 bicyclist and is the answer

4 trike riders (12 wheels) + 7 bike riders (14 wheels) = 11 people and 26 wheels

Not enough information