You know what’s funny, is I “get” that totally looking at your breakdown, particularly at the check your work part, but the logical inconsistency created by “dogs” as a set ending with a fractional algebraic answer seems to screw with the mind.
“the logical inconsistency created by ‘dogs’ as a set ending with a fractional algebraic answer seems to screw with the mind”
It is clear that the educators messed up here. The math is too sophisticated for most children of that age. Counting dogs in a show strongly implies whole numbers only.
Either something was left out, like number of medium dogs, or they simply should have left out the “more... than” and pegged the small dog count at 36, and said to solve for the large dog count. Simple age-appropriate subtraction.